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Applied Probability Days

Date: FRIDAY, APRIL 25, 2014

Room 303
S. W. Mudd Building
500 W. 120th St.
Columbia University
New York City

Registration is FREE, all are welcome to join! (But please RSVP: [email protected])

SPEAKERS & SCHEDULE

Date: FRIDAY DECEMBER 2, 2011

Room 303
S. W. Mudd Building
500 W. 120th St.
Columbia University
New York City

Registration is FREE, all are welcome to join! 
Click HERE to register.

EVENT POSTER

SPEAKERS & SCHEDULE

Friday July 10, 2009

1:00PM-4:00PM

Room 833
S.W. Mudd Building
500 West 120th Street
Columbia University, New York City

REGISTRATION IS FREE, all are very welcome, please join.

SPEAKERS & SCHEDULE

CLICK HERE TO VIEW POSTER

For more information,  please contact:
Karl Sigman
CAP Director [email protected]

IN HONOR OF CHRIS C. HEYDE

In Memoriam: Christopher C. Heyde (1939 – 2008)

Saturday, June 28th, 2008 
9:00AM-6:00PM

Columbia University, New York City 
(Location: Room 303 in S.W. Mudd Building)

SPEAKERS:

Five (5) Speakers include:

  • David Pollard, Yale University, USA
    Random chromatic numbers, some statistical folklore, and some puzzling inequalities
  • Søren Asmussen, Aarhus University, Denmark
    Failure probabilities for checkpointing and parallel computing
  • Steve Kou, Columbia University, USA
    The Recent Financial Turmoil and Related Financial Engineering Research Problems
  • J. Michael Steele, Wharton School, USA
    Martingale Markets
  • Sidney Resnick, Cornell University, USA
    Multivariate regular variation on 3 cones yields three theories

SCHEDULE:

We particularly warmly welcome all of those who remember Chris C. Heyde; his students, his colleagues and his friends. 
To Register:
REGISTRATION IS FREE, all are very welcome; 
but please email [email protected] to let us know that you plan to attend.

History:
Applied Probability Day (APD) first took place in April 1992 at Columbia University as a one-day international event and has been successfully repeated annually since. It traditionally takes place on a Friday 9:00am-6:00pm, but this year it will be on a Saturday.

For inquiries: 
[email protected] (Karl Sigman)

Applied Probability Day 1992-2007

Friday June 8th, 2007 
9:00AM-6:00PM

Columbia University, New York City 
(Location: Room 303 in S.W. Mudd Building)

SCHEDULE

TO REGISTER:

REGISTRATION IS FREE, all are very welcome; 

but please email [email protected] to let us know that you plan to attend.

HISTORY:

Applied Probability Day (APD) first took place in April 1992 at Columbia University as a one-day international event and has been successfully repeated annually since. It traditionally takes place on a Friday 9:00am-6:00pm, leaving the weekend free for visitors to enjoy the many attractions of New York City.

FRIDAY MAY 12
DAVIS AUDITORIUM, COLUMBIA UNIVERSITY

View Poster of Conference

Schedule of Events

  • 9:15 - 10:00 Poisson Process Approximation: from Palm theory to Stein's method

    Louis H Y Chen 
    Institute for Mathematical Sciences
    National University of Singapore 

    Poisson process approximation using Stein's method has been successfully developed by Barbour, Brown, Xia and others since 1988. The key idea is to convert the Stein equation to one involving the generator of an immigration-death process whose equilibrium distribution is the approximating Poisson process, solve the equation in terms of the immigration-death process and then obtain sharp bounds on the solution and its smoothness by using coupling. This approach is known as the probabilistic approach of Barbour. 

    In this talk, the probabilistic approach of Barbour is used but the framework of Stein's method is presented from the point of view of Palm theory, which is used to construct Stein identities and define local dependence of point processes. A Wasserstein pseudo-metric is also defined and applied to certain point processes which can be viewed as locally dependent by enlarging the carrier space. 

    Poisson process approximation theorems are proved for locally dependent point processes as well as for dependent superposition of point processes. The theorems are applied to Matern hard-core processes, words in DNA and superposition of renewal processes. 

    This talk is based on joint work with Aihua Xia. 

  • 10:00 - 10:45 Stochastic Batch Scheduling and the "Smallest Variance First" Rule

    Michael Pinedo
    Stern School of Business
    New York University

    Consider a single machine that can process multiple jobs in batch mode. We have n jobs and the processing time of job j is a random variable X_j with distribution F_j. Up to b jobs can be processed simultaneously by the machine. The jobs in a batch all have to start at the same time and the batch is completed when all jobs have finished their processing (i.e., at the maximum of the processing times of the jobs in that batch). We are interested in two objective functions, namely the minimization of the expected makespan and the minimization of the total expected completion time. We first show that under certain fairly general conditions the minimization of the expected makespan is equivalent to specific deterministic combinatorial problems, namely the Weighted Matching problem and the Set Partitioning problem. We then consider the case when all jobs have the same mean processing time, but different variances. We show that for certain special classes of processing time distributions the "Smallest Variance First" rule minimizes the expected makespan as well as the total expected completion time. In our conclusions we present various general rules that are suitable for the minimization of the expected makespan and the total expected completion time in batch scheduling.

  • 11:15 - 12:00 Stochastic Modeling in Nanoscale Biophysics

    Samuel Kou
    Harvard University

    Recent advances in nanotechnology allow scientists to follow a biological process on the individual molecule basis. These advances also raise many challenging stochastic modeling problems, because the experimental capability of zooming in on single molecules reveal that many classical models derived from oversimplified assumptions are no longer valid. One such phenomenon that we will focus in the talk is that of subdiffusion, which much departs from the classical Brownian diffusion theory. By introducing fractional Gaussian noise (i.e. the derivative of fractional Brownian motion) into the generalized Langevin equation, we propose a model to describe subdiffusion. In addition to analytical tractability and clear physical meaning, this model is capable of explaining the experimentally observed conformational fluctuation in enzyme reactions. Excellent agreement between the model prediction and the single-molecule experimental data is seen. 

  • 2:00 - 2:45 On Ruin Probability for a Risk Process with Phase-type Claims and Inter-arrival Times Perturbed by a Levy Process with No Negative Jumps

    Esther Frostig
    University of Haifa, Israel 

    We study a risk process where the claim size and the inter-arrival times are phase-type distributed. The risk process is perturbed by a Levy process without negative jumps. We show that the ruin probability, and the distribution of deficit at ruin, are the same as in an unperturbed risk model with general inter-arrival times and phase type claim size, where the inter-arrival times and the claims are dependent. The model is analyzed via the dual queueing system. We show that the dual queueing system is a Markov arrival process. queueing system. 

  • 2:45 - 3:30 A Levy Process Reflected at a Poisson Age Process

    Offer Kella
    Hebrew University of Jerusalem

    We consider a Levy process with no negative jumps, reflected at a stochastic boundary which is a positive constant multiple of an age process associated with a Poisson process. We show that the stability condition for this process is identical to the one for the case of reflection at the origin. In particular, there exists a unique stationary distribution which is independent of initial conditions. We identify the Laplace-Stieltjes transform of the stationary distribution and observe that it satisfies a decomposition property. In fact, it is a sum of two independent random variables, one of which has the stationary distribution of the process reflected at the origin, and the other has the stationary distribution of a certain clearing process. The latter is itself distributed like an infinite sum of independent random variables. Finally, we discuss the tail behavior of the stationary distribution and in particular observe that the second distribution in the decomposition always has a light tail. This talk is based on joint work with Onno Boxma and Michel Mandjes. 

  • 4:00 - 4:45 Sampling and Estimation from Heavy Tailed Distributions in the Internet

    Nick Duffield
    AT&T 

    Internet service providers commonly collect usage data in the form of flow records that summarize sets of related packets passing through routers. Speed and bandwidth constraints in the measurement and analysis infrastructure necessitate that the flow records be sampled to reduce data volumes and increase query speed. A relatively small proportion of these flow records represent a large proportion of the traffic. This talk reviews some approaches to the problem of how best to sample and estimate from these flow records.

Monday May 10th, 2004 
9:00AM-6:00PM

Columbia University, New York City 
(Location: Interschool Lab, 7th Floor of CEPSR (Shapiro Engineering Center)) 

Schedule

TO REGISTER:

REGISTRATION IS FREE, all are very welcome; 
but please email [email protected] to let us know that you plan to attend. 

HISTORY:

Applied Probability Day (APD) first took place in April 1992 at Columbia University as a one-day international event and has been successfully repeated annually since. It traditionally takes place on a Friday (although it is on a Monday this year), 9:00am-6:00pm, leaving the weekend free for visitors to enjoy the many attractions of New York City.

For inquiries: 
[email protected] (Chris Heyde, Director of CAP) 
[email protected] (Karl Sigman, Secretary of CAP)

Friday April 4, 2003 
9:00AM-6:00PM

Columbia University, New York City 
(Location: Interschool Lab, 7th Floor of CEPSR (Shapiro Engineering Center))

DOWNLOAD POSTER (.pdf)

SCHEDULE

TO REGISTER:

REGISTRATION IS FREE, all are very welcome; 
but please email [email protected] to let us know that you plan to attend. 
 

HISTORY:

Applied Probability Day (APD) first took place in April 1992 at Columbia University as a one-day international event and has been successfully repeated annually since. It traditionally takes place on a Friday (although it is on a Thursday this year), 9:00am-6:00pm, leaving the weekend free for visitors to enjoy the many attractions of New York City.
 

For inquiries: 
mailto:[email protected] (Chris Heyde, Director of CAP) 
[email protected] (Karl Sigman, Secretary of CAP)

Applied Probability Day 1992-2000

Thursday May 9, 2002 
9:00AM-6:00PM

C.P. Davis Alumni Auditorium 
Morris A. Shapiro Center forEngineering and Applied Science Research 
Room 412 
Columbia University, New York City. 

Shedule

TO REGISTER:

REGISTRATION IS FREE, all are very welcome; 
but please email [email protected] to let us know that you plan to attend. 
 

HISTORY:

Applied Probability Day (APD) first took place in April 1992 at Columbia University as a one-day international event and has been successfully repeated annually since. It traditionally takes place on a Friday (although it is on a Thursday this year), 9:00am-6:00pm, leaving the weekend free for visitors to enjoy the many attractions of New York City.

Directions and parking information 
 

For inquiries: 
mailto:[email protected](Chris Heyde, Director of CAP) 
[email protected] (Karl Sigman, Secretary of CAP

 

Friday April 6, 2001, 9:00AM-6:00PM 
C.P. Davis Alumni Auditorium 
Morris A. Shapiro Center for 
Engineering and Applied Science Research 
Room 412 
Columbia University, New York City. 

Schedule

TO REGISTER:

REGISTRATION IS FREE, all are very welcome; 
but please email [email protected] to let us know that you plan to attend. 
 

HISTORY:

Applied Probability Day (APD) first took place in April 1992 at Columbia 
University as a one-day international event and has been successfully repeated 
annually since. It traditionally takes place on a Friday, 9:00am-6:00pm, 
leaving the weekend free for visitors to enjoy the many attractions of New York City.

For inquiries: 
[email protected] (Chris Heyde, Director of CAP) 
[email protected] (Karl Sigman, Secretary of CAP)

 

Friday May 5, 2000, 9:00AM-6:00PM 
C.P. Davis Alumni Auditorium 
Morris A. Shapiro Center for 
Engineering and Applied Science Research 
Room 412 
Columbia University, New York City. 

Schedule

This event will be preceded by BENESFEST , a day of stochastic control in honor of Vaclav E. Benes.

For inquiries: 
[email protected] (Chris Heyde, Director of CAP) 
[email protected] (Karl Sigman, Secretary of CAP)

Applied Probability Day (APD) first took place in April 1992 at Columbia University as a one-day international event. It traditionally takes place on a Friday, 9:00AM - 6:00PM, leaving the weekend free for visitors to enjoy the many attractions of New York City.  In 1995 APD was merged together with the fall semester of Probability Towards 2000.

Each APD has six renown invited speakers covering a broad array of topics in applied probability. Previous speakers and the titles of their talks are listed below: 

APD 1992:

  • Joel E. Cohen (Rockefeller U.): Random Graphs in Biology
  • Rick T. Durrett (Cornell U.): Particle System Models of Ecosystem Dynamics
  • Frank P. Kelly (Cambridge U.): Network Routing
  • Charles M. Newman (Courant Institute, New York U.): Maximum Path Lengths for Random Task Graphs
  • Lawrence A. Shepp (ATT Bell Labs): Some Problems in Applied Probability
  • William D. Sudderth (U. Minnesota): Approximation Theorems and Algorithms in Gambling Theory and Stochastic Games

APD 1993:

  • David Aldous (U. Calif. Berkeley): Some Open Problems on Reversible Finite Markov Chains
  • Mark H. A. Davis (Imperial College): A Deterministic Approach to Stochastic Optimal Control
  • Persi Diaconis (Harvard U.): Haar Measure for Probabilists
  • Murad Taqqu (Boston U.): Self-Similar Processes with Infinite Variance
  • S.R.S. Varadhan (Courant Institute, New York U.): Hydrodynamic Scaling: The Transition From Particles to Fluid
  • Ward Whitt (AT&T Bell Labs): The Nonstationary Erlang Loss Model

APD 1994:

  • Ed Coffman (AT&T Bell Labs): Stochastic Matching: Guises and Applications
  • Cristina Costantini (U. Rome, Italy): The Skorohod Reflection Problem
  • Robin Pemantle (U. Wisconsin, Madison): What is the Probability that a Markov Chain Hits a Set?
  • Steve Shreve (Carnegie Melon U.): Heavy Traffic Convergence of a Controlled Multi-Class Queueing System
  • Mike Steele (Wharton School, U. Pennsylvania): Problems and Progress in Probability and Algorithms
  • Simon Tavare (U. Southern Calif.): When did Eve Live?--Ancestral Inference in Population Genetics

APD 1996:

  • Erhan Cinlar (Princeton U.): Stochastic models of turbulent transport
  • Claudia Kl&uumlppelberg (Johannes Gutenberg U., Mainz, Germany): Subexponential distributions revisited
  • Robert Adler (U. North Carolina, Chapel Hill): Building with superprocesses
  • Debasis Mitra (AT&T Bell Labs): Some recent approaches and results on broadband network design
  • Michel Talagrand (Ohio State U. and C.N.R.S., France): An inequality for the Sherrington Kirkpatrik spin glass model
  • Michael Waterman (U. Southern Calif.): Oceans and islands in DNA physical maps

APD 1997:

  • W. J. Ewens (U. Pennsylvania):
  • Statistical Problems in Human Genetics
  • Jeff Steif (U. Göteborg, Sweden):
  • Phase Transitions for Markov Random Fields: Some Results and Open Questions
  • Marcel F. Neuts(U. of Arizona, Tucson):
  • The Case for Computer Experimentation in Stochastic Modelling
  • J. Michael Harrison(Stanford U.):
  • Brownian Models of Stochastic Processing Networks
  • Jean Walrand(U. California, Berkeley):
  • Models and Problems in High-performance Communication Networks
  • Donald L. Turcotte(Cornell U.):
  • Self-Organized Criticality and the Statistics of Natural Hazards

APD 1998:

  • Jonathan Goodman(Courant Institute, New York U.)
  • New Monte Carlo methods for value at risk and stochastic differential equ\ ations
  • Philip Heidelberger(IBM, Watson Research Center)
  • Multilevel splitting for estimating rare event probabilities
  • Sidney Resnick (Cornell U.)
  • Why the sample correlation function will break your heart
  • Paul Dupuis (Brown U.)
  • Simple necessary and sufficient conditions for the stability of constrained processes
  • Marc Yor(Paris VI, France)
  • Some combinations of Asian, Parisian and Barrier options
  • Freddy Delbaen(ETH Zurich, Switzerland)
  • Passport options: Russian and Asian relations

APD 1999

  • Soren Asmussen, University of LundSweden
  • Exponential Martingales in Applied Probability
  • Rene A. Carmona, Princeton UniversityUSA
  • Transport by Stochastic Flows: Rigorous Results, Simulations and Conjectures.
  • Benoit Mandelbrot, Yale UniversityUSA
  • Multifractal Properties of Financial Prices
  • Don Dawson, Fields Institute, Toronto, Canada
  • Measure-valued Models of Catalytic and Mutually Catalytic Branching
  • Thomas Liggett, UCLAUSA
  • Contact Processes on Lattices and Trees
  • Ruth Williams, UC San Diego, USA
  • Reflecting Diffusions and Queueing Networks

APD 2000

  • D. Bertsimas, Massachusetts Institute of Technology
  • Moment Problems and Their Applications
  • D. HeathCarnegie Mellon University
  • Risk Management Using Coherent Risk Measures
  • T. KurtzUniversity of Madison, Wisconsin
  • Exchangeability and derivation and approximation of filtering equations
  • P. ProtterPurdue University
  • Non-redundant Claims:  Robustness, Regularity, and Formulas
  • D. Siegmund, Stanford Univerity
  • Approximate P-values for Local Sequence  Alignments
  • R. WeberCambridge University
  • A Large Deviations Analysis of the Multiplexing of Periodic Traffic Sources
  • Soren AsmussenUniversity of Lund, Sweden
  • Exponential Martingales in Applied Probability

APD 2001

  • Richard Tweedie, U. Minnesota
  • Drift Conditions for Stability of Markov Chains (revisited)
  • Marty Reiman, Lucent Technologies
  • A Comparison of Two Heavy Traffic Regimes for Multiserver Queues
  • Daniel Ocone, Rutgers U.
  • Recent Problems in Stochastic Control
  • Richard Gill, U. Utrecht, Eurandom, Netherlands
  • Teleportation Into Quantum Statistics
  • Ragnar Norberg, LSE, London, UK
  • Pricing and Hedging in Life and Pension Insurance
  • Per Mykland,UChicago
  • Trading Options with Statistical Prediction Intervals

APD 2002

  • Michael Rabin, Harvard U. & Columbia U.
  • Provably Information Secure Encription
  • Francois Baccelli, INRIA & ENS, Paris, France
  • A Probabilistic Model of Congestion Control in the Internet
  • Thaleia Zariphopolou, U. Texas
  • Indifference Prices and Optimal Investments
  • Victor Solo, U. New South Wales, Sydney, Australia
  • Neural Receptive Field Plasticity via Point Process Adaptive Filtering
  • Edward WaymireOregon State U.
  • A Probabilistic View of Navier-Stokes and Related Equations
  • Peter Glynn, Stanford U. Brownian Traffic Modeling

APD 2003

  • Cheng-Der Fuh, Inst. of Statistical Science, Academia Sinica, Taiwan
  • SPRT and CUSUM in Hidden Markov Models
  • Harold Kushner, Brown University
  • Proportional Fair Sharing Algorithms for Mobile Communications
  • Philippe Robert, INRIA, Rocqencourt, France
  • Stochastic models of data transmission in communication networks
  • George Moustakides, IRISA - INRIA, Rennes, France
  • Optimum CUSUM tests for detecting changes in continuous time processes
  • John P. LehoczkyCarnegie Mellon University
  • Heavy Traffic Limit Theorems for Real-Time Computer Systems
  • Alexander StolyarBell Labs Research
  • Scheduling of Flexible Interdependent Time-varying Servers

 APD 2004

  • Assaf Naor (Microsoft Research):Shannon's Problem on the Monotonicity of Entropy
  • Yuval Peres (UC Berkeley): A Stable Marriage of a Poisson Process and Lebesgue Measure
  • Amir Dembo (Stanford University):Fractal geometry of simple random covering: late and favorite points
  • Timo Seppalainen (University of Wisconsin): Inhomogeneities and the Hydrodynamic Limit of the Asymmetric Exclusion Process
  • Gennady Samorodnitsky (Cornell University): Measuring the Length of Memory in Infinite Variance Stable Processes
  • Chris Heyde (Columbia University and Australia National University): The Zoo of Non-classical Limit Theorems - Species Yet to be Classified

APD 2006

  • H. Chen (National University of Singapore): Poisson Process Approximation: from Palm theory to Stein’s method
  • Michael Pinedo (Stern School of Business, New York University ): Stochastic Batch Scheduling and the “Smallest Variance First Rule
  • Samuel Kou (Harvard University): Stochastic Modeling in Nanoscale Biophysics
  • Frostig (University of Haifa): On Ruin Probability for a Risk Process with Phase-type Claims and Inter-arrival Times Perturbed by a Levy Process with No Negative Jumps
  • Offer Kella (The Hebrew University of Jerusalem): A Levy Process Reflected at a Poisson Age
  • Nick Duffield (AT&T Labs Research): Sampling and Estimation from Heavy Tailed Distributions in the Internet

APD 2007

  • Kevin Glazebrook (Lancaster U., UK): General Notions of Indexability and Dynamic Allocation of Individuals to Teams Providing Service
  • Jose Blanchet (Harvard U.): Rare-event Analysis and Simulation of Heavy-tailed Systems
  • Jim Fill (Johns Hopkins U.): A (Minor) Miracle: Diagonalization of a Bose-Einstein Markov Chain
  • Marco Avellaneda (Courant Institute, NYU): Power-Law Price Impact Models and Stock Pinning on Option Expiration Dates
  • Steve Lalley (U. Chicago): Spatial Epidemics: Critical Behavior
  • Les Servi (Lincoln Labs, MIT): Methods of Maritime Tracking: An Overview from an Applied Probability/Operations Research Perspective

Cap Workshops

COLUMBIA QUANTITATIVE TRADING AND ASSET MANAGEMENT WORKSHOP

Friday, November 19, 2010
Davis Auditorium, 412 Schapiro Center (CEPSR), Columbia University

Hosted by: The Center for Applied Probability (CAP), The Center for Financial Engineering (CFE) and The Program for Financial Studies.

Schedule

 

Hosted by
The Center for Financial Engineering and The Center for Applied Probability (CAP) at Columbia University

THE CENTER FOR FINANCIAL ENGINEERING AND THE CENTER FOR APPLIED PROBABILITY (CAP) AT COLUMBIA UNIVERSITY PRESENT:THE 15TH ANNUAL WORKSHOP ON DERIVATIVE SECURITIES & RISK MANAGEMENT

Friday, December 5th, 2008, Columbia University, New York City
Location: Uris Hall, Room 301
9:00 AM--6:00 PM

SPEAKERS:

Robert Almgren, (Courant Institute of Mathematical Sciences, New York University)

“Quantitative Challenges In Algorithmic Trading”

Christoph Burgard, Global Head of Equities, Credit, Credit-Counterparty and Emerging Markets Quantitative Analytics, Barclays Capital

"New Developments In Volatility And Variance Products Pricing And The Link To Forward Volatility."

Jianqing Fan, (Professor of Finance, Director of Committee of Statistical Studies, Princeton University)

“Risk Assessment And Asset Allocation With Gross Exposure Constraints For Vast Portfolios”

Jean-David Fermanian, (Senior Quantitative Analyst, BNP Paribas)

"On Break Even Correlation: The Way To Price Structured Credit Derivatives By Replication."

Fabio Mercurio (Senior Researcher, Bloomberg L.P.)

“Market Models for Inflation Derivatives”

Attilio Meucci, (Head of Portfolio Research, Bloomberg L.P.)

“Fully Flexible Views: Theory And Practice”

Peter Tankov  (Associate Professor, Ecole Polytechnique)

“Pricing And Hedging Gap Risk”

Jiang Wang, Professor, MIT Sloan School of Management

“Asset Pricing And The Credit Market”

Johannes Wissel (Visiting Assistant Professor, Cornell University)

“Arbitrage-free Market Models For Liquid Options”
 

REGISTRATION

REGISTRATION FEES:

Academic:
$175 ($100 student)

Corporate & Institutional:
$350

PAYMENTS:

If paying by credit card, please click on the link below:
https://calendar.columbia.edu/sundial/webapi/register.php?eventID=27313

If paying by check, make checks payable to:
Center for Financial Engineering, Columbia University

Mail Checks to:
Industrial Engineering & Operations Research Department
Columbia University
500 West 120th Street Room 313 Mudd
New York, NY 10027
Attn: Donella Crosgnach

Co-sponsored by the Center for Financial Engineering

FRIDAY, NOVEMBER 9TH, 2007

DAVIS AUDITORIUM
COLUMBIA UNIVERSITY

SCHEDULE OF EVENTS

9:00 - 9:45 Local Volatility Dynamic Models  [DOWNLOAD]            

Rene Carmona
Professor, Operations Research & Financial Engineering 
Princeton University Bendheim Center for Finance      

This paper is concerned with the characterization of arbitrage free dynamic stochastic models for the equity markets when Ito stochastic differential equations are used to model the dynamics of a set of basic instruments including, but not limited to, theunderliers. We study these market models in the framework of the HJM philosophy originally articulated for Treasury bond markets. The approach to dynamic equity models which we follow was originally advocated by Derman and Kani in a rather informal way. The present paper can be viewed as a rigorous development of this program, with explicit formulae, rigorous proofs and numerical examples.                                                                    

9:45 - 10:30 H2: A New Concept in Risk Management    

Bruno Dupire
Senior Researcher 
Bloomberg LP

How risky is an ITM barrier option? How can we hedge a basket or spread options with options on the components? Pricing by perfect replication is a very potent tool but real markets are far from being complete and most contingent claims cannot be perfectly hedged. We define a measure of hedge efficacy, H2 (in reference to the R2 of a regression), which reflects the reduction of tracking error variance when using a certain set of hedging instruments/strategies. We illustrate the approach in the case of discrete time hedging, stochastic volatility and multi-asset  models.

11:00 - 11:45 Pricing Swaps and Options on Quadratic Variation Under Stochastic Time Change Models   [DOWNLOAD]      

Andrey Itkin
Head of Quantitative Strategies / Adjunct Professor 
Volant Trading / Rutgers University

Swaps and options on quadratic variation recently became very popular instruments at financial markets. However, there exists a known observation that simple models are not able to replicate the price of the quadratic variation contract for all maturities. Therefore, one can see a steadfast interest to applying more sophisticated jump-diffusion and stochastic volatility models to pricing swaps and options on the quadratic variation. Usually Monte-Carlo methods are used to price the quadratic variation products under this approach, because analytical and semi-analytical (like FFT) results are available only for the simplest models. In the present paper we consider a class of models that are known to be able to capture at least an average behavior of the implied volatilities of the stock price across moneyness and maturity time-changed Levy processes. For these models we derive an analytical expression for the fair value of the quadratic variation and volatility swap contracts as well as use a modifyedCarr-Madan FFT approach proposed by Roger Lee to price options on these products. The results are compared with the market data.

11:45 - 12:30 Default Correlation, Cluster Dynamics and Single Names: The GPCL Dynamical Loss Model   

Damiano Brigo 
Managing Director & Global Head, Quantitative Structured Credit Innovation
DerivativesFitch

We extend the common Poisson shock framework reviewed for example in Lindskog and McNeil (2003) to a formulation avoiding repeated defaults, thus obtaining a model that can account consistently for single name default dynamics, cluster default dynamics and default counting process. This approach allows one to introduce significant dynamics, improving on the standard “bottom-up” approaches, and to achieve true consistency with single names, improving on most “top-down” loss models. Furthermore, the resulting GPCL model has important links with the previous GPL dynamical loss model in Brigo, Pallavicini and Torresetti (2006a,b), which we point out. Model extensions allowing for more articulated spread and recovery dynamics are hinted at. Calibration to both DJi-TRAXX and CDX index and tranche data across attachments and maturities shows that the GPCL model has the same calibration power as the GPL model while allowing for consistency with single names.

2:00 - 2:45 Latest Research on Liquidity Risk - Topic to be Announced  [DOWNLOAD]

Lasse Pedersen
Professor, Finance 
NYU Stern School of Business

TBA

2:45 - 3:30 Equity Correlation Swaps: A New Approach for Modeling & Pricing   [DOWNLOAD] 

Sebastien Bossu
Vice President, Equity Derivatives Structuring
Dresdner Kleinwort

Correlation Swaps were introduced in the early 2000's to allow investors to bet on realized correlation against a strike, and help exotic derivative desks to recycle their correlation risk. In practice the strike is driven by supply and demand and may differ significantly from the implied correlation derived from the prices of vanilla options on indices and their constituent stocks. In this presentation we introduce some fundamental relationships for realized and implied correlation, propose a simple model for derivatives on variance and proceed to derive the arbitrage strike of index correlation swaps based on dynamic trading of variance dispersions. The conclusion is that the fair strike is close to implied correlation, revealing potential dynamic arbitrage opportunities in the market.

4:00 - 4:45 Efficient Risk Management in Monte Carlo   [DOWNLOAD]   

Luca Capriotti
Global Modeling & Analytics Group
Credit Suisse 

Monte Carlo simulations are an indispensable tool for pricing and hedging derivatives securities due to the ever increasing level of sophistication of the instruments traded in the Financial Markets. Although generally straightforward to implement, Monte Carlo approaches carry a very significant computational cost. In this talk, I will describe some recent research aimed at improving the efficiency of the Monte Carlo calculation of Option Prices and Sensitivities (so-called Greeks) by means of Importance sampling, Likelihood Ratio Methods, and Adjoint techniques. 

4:45 - 5:30 Optimal Disclosure and Operational Risk: Evidence from Hedge Fund Registration   [DOWNLOAD]

William Goetzmann
Professor, Fiance
Yale School of Management 

Required disclosure is an important regulatory tool in that it allows market participants to assess manager risks without constraining manager actions. This trade-off between freedom of activity and transparency is particularly relevant to hedge funds, which rely often rely on proprietary models and positions. We use the recent, unsuccessful SEC attempt to increase hedge fund disclosure through registration in order to examine the value of disclosure to investors. We test the potential value and materiality of operational risk and conflict of interest variables disclosed in Form ADV filed by a large number of hedge funds in February 2006. We find that operational risk indicators are conditionally correlated to conflict of interest variables, indicating a potential value of disclosing such conflicts to investors. Operational risk factors are also correlated to lower leverage and concentrated ownership, suggesting that the 2006 disclosure requirements may have been redundant for lenders and equity investors in hedge funds. In contrast, operational risk factors had no ex-post effect on the flow-performance relationship, suggesting that investors either lack this information, or they do not regard it as material. The findings suggests that any consideration of disclosure requirements should take into account the endogenous production of information within the industry, and the marginal benefit of required disclosure on different investment clienteles.

 

Registration :
REGISTRATION FEES:

Academic Rates:
Before Oct. 12: $125 ($40 student)
On site: $175 ($100 student)

Corporate Rates:
Before Oct. 12: $225
On site: $325

Credit Cards (Visa/Mastercard), Checks (made payable to Center for Applied Probability), or Money Orders are accepted.

Please contact Administrative Coordinator Emmanuel Casuscelli at [email protected] or (212)-854-8404 to register.

Hotel Arrangements:
For hotels near Columbia University , please visit:  http://www.campustravel.com/university/columbia/

For Inquiries:
[email protected] (Chris Heyde, Director of CAP)
[email protected] (Karl Sigman, Secretary of CAP)

Friday, October 28, 2005 
Columbia University, New York City.

This year's workshop again features a group of distinguished speakers in an informal setting aimed at fostering communication between academia and industry. 

Schedule

 

REGISTRATION FEES:

Academic: 
Before Oct. 12: $125 ($40 student) 
On site: $175 ($100 student)

Corporate: 
Before Oct. 12: $225 
On site: $325 
 

A light lunch will be provided, and a wine and cheese reception will be held at the end of the day.

REGISTRATION PROCEDURE:

Send Name, Title, Affiliation, Address and E-mail Address (as we prefer to acknowledge receipt of your registration by e-mail), along with a check or money order payable to Columbia University to the address below.

Or, to pay by credit card (MC or Visa ONLY), send the same information in an e-mail to the address below and, in addition, include CC#, Exp. Date, Name (as it appears on card), and Billing Address. If you prefer, you may FAX the information, or a legible (not too dark) copy of your credit card, to the FAX number listed below.

CONTACT:

E-mail: [email protected] 
cap.columbia.edu/ 
Postal: Center for Applied Probability, ATTENTION: Finance Workshop 
331 Mudd Building, Columbia University, Mail code 4704 
500 West 120th Street, New York, NY 10027 
Phone: (212) 854-6096 
FAX: (212) 854-8103

LOCATION:

Davis Auditorium 
Fourth Floor Shapiro Center 
Map

Organizers:

M. Broadie, E. Derman, P. Glasserman, C. Heyde, S. Kou, and K. Sigman 
 

For general CAP inquiries: 
[email protected] (Chris Heyde, Director of CAP) 
[email protected] (Karl Sigman, Secretary of CAP)

Friday, November 5, 2004 
Columbia University, New York City.

This year's workshop again features a group of distinguished speakers in an informal setting aimed at fostering communication between academia and industry. 
 

SPEAKERS:

Rama Cont, Ecole Polytechnique 
Numerical Methods for Option Pricing Models with Jumps

David Hobson, Princeton University 
Extending Figlewski's Option Pricing Formula

Michael Kalkbrener, Deutschebank 
A Quantitative Framework for Measuring Risk and Profitability

Ozgur Kaya, Columbia University 
Exact Simulation of Financial Models with Stochastic Volatility and other Affine Jump Diffusion Processes

Jussi Keppo, University of Michigan 
Does the Market Risk Capital Requirement Affect Bank Behavior?

Roger Lee, Stanford University 
Robust Hedging of Volatility Derivatives

Richard Martin, Credit Suisse First Boston 
Developments in Credit Portfolio Theory

H. Eugene Stanley, Boston University 
Understanding Large Movements in Stock Market Activity 
 

Download poster with schedule of events 
 

REGISTRATION FEES:

Academic: 
Before Oct. 24: $125 ($40 student) 
On site: $175 ($100 student)

Corporate: 
Before Oct. 24: $225 
On site: $325 
 

A light lunch will be provided, and a wine and cheese reception will be held at the end of the day.

REGISTRATION PROCEDURE:

Send Name, Title, Affiliation, Address and E-mail Address (as we prefer to acknowledge receipt of your registration by e-mail), along with a check or money order payable to Columbia University to the address below.

Or, to pay by credit card (MC or Visa ONLY), send the same information in an e-mail to the address below and, in addition, include CC#, Exp. Date, Name (as it appears on card), and Billing Address. If you prefer, you may FAX the information, or a legible (not too dark) copy of your credit card, to the FAX number listed below.

CONTACT:

E-mail: [email protected] 
cap.columbia.edu/ 
Postal: Center for Applied Probability, ATTENTION: Finance Workshop 
331 Mudd Building, Columbia University, Mail code 4704 
500 West 120th Street, New York, NY 10027 
Phone: (212) 854-6096 
FAX: (212) 854-8103

LOCATION:

Davis Auditorium 
Fourth Floor Shapiro Center 

Organizers:

M. Broadie, E. Derman, P. Glasserman, C. Heyde, S. Kou, and K. Sigman 

For general CAP inquiries: 
[email protected] (Chris Heyde, Director of CAP) 
[email protected] (Karl Sigman, Secretary of CAP)

Friday, November 7, 2003 
Columbia University, New York City.

This year's workshop again features a group of distinguished speakers in an informal setting aimed at fostering communication between academia and industry. 
 

SPEAKERS:

KEYNOTE SPEAKER: 
Robert Jarrow, Cornell 
    "A Reduced Form Theory of the Firm"

Marco Avellaneda, NYU 
    "A market-induced mechanism for stock pinning" 
Jean-Pierre Fouque, North Carolina State 
    "Multiscale stochastic volatility" 
Kay Giesecke, Cornell 
    "The Market Price of Credit Risk" 
Vicky Henderson, Princeton 
    "A comparison of q-optimal option prices in a stochastic volatility model with correlation" 
David Li, Citigroup 
    "Pricing and hedging synthetic CDO transactions" 
Vladimir Piterbarg, Bank of America 
    "Pricing and hedging callable Libor exotics in forward Libor models" 
Barry Schacter, SAC Capital 
    "Problems of performance measurement in hedge funds" 
 

Download poster with schedule of events 
 

REGISTRATION FEES:

Academic: 
Before Oct. 24: $125 ($40 student) 
On site: $175 ($100 student)

Corporate: 
Before Oct. 24: $225 
On site: $325

A light lunch will be provided, and a wine and cheese reception will be held at the end of the day.

REGISTRATION PROCEDURE:

Send Name, Title, Affiliation, Address and E-mail Address (as we prefer to acknowledge receipt of your registration by e-mail), along with a check or money order payable to CAP to the address below.

Or, to pay by credit card (MC or Visa ONLY), send the same information in an e-mail to the address below and, in addition, include CC#, Exp. Date, Name (as it appears on card), and Billing Address. If you prefer, you may FAX the information, or a legible (not too dark) copy of your credit card, to the FAX number listed below.

CONTACT:

E-mail: [email protected] 
cap.columbia.edu
Postal: Center for Applied Probability, ATTENTION: Finance Workshop 
331 Mudd Building, Columbia University, Mail code 4704 
500 West 120th Street, New York, NY 10027 
Phone: (212) 854-6096 
FAX: (212) 854-8103

LOCATION:

Schermerhorn Hall 
Room 501 

Organizers:

M. Broadie, P. Glasserman, C. Heyde, S. Kou, and K. Sigman 

For general CAP inquiries: 
[email protected] (Chris Heyde, Director of CAP) 
[email protected] (Karl Sigman, Secretary of CAP)

Friday, November 1, 2002 
Columbia University, New York City. 
(This web site was updated on September 13, 2002)

This year's workshop again features a group of distinguished speakers in an informal setting aimed at fostering communication between academia and industry. 
 

SPEAKERS:

Alan Brace, BNP Paribas 
    "Markovian Models in the Stochastic Implied Volatility Framework" 
Pierre Collin-Dufresne, Carnegie-Mellon University 
    "Generalizing the Affine Framework to HJM and Random Field Models" 
Jaksa Cvitanic, University of Southern California 
    "An Intertemporal Model of Active Portfolio Management" 
Craig Friedman, Standard & Poors 
    "Learning Models for Credit Risk" 
Martin Haugh, Columbia University 
    "Hedging Financial Risks in Supply Chain Management" 
Marco Naldi, Lehman Brothers 
    "CDO Analysis: Beyond the CADR Assumption" 
Dmitry Pugachevsky, Bear Stearns 
    "Efficient Modeling of Default Correlations" 
Carlos Sin, UBS Warburg 
    "Interest Rate Models that are Stable Under Measure Change"

REGISTRATION FEES:

Academic: 
Before Oct. 18: $100 ($40 student) 
On site: $150 ($100 student)

Corporate: 
Before Oct. 18: $200 
On site: $300

A light lunch will be provided, and a wine and cheese reception will be held at the end of the day.

REGISTRATION PROCEDURE:

Send Name, Title, Affiliation, Address and E-mail Address (as we prefer to acknowledge receipt of your registration by e-mail), along with a check or money order payable to CAP to the address below.

Or, to pay by credit card (MC or Visa ONLY), send the same information in an e-mail to the address below and, in addition, include CC#, Exp. Date, Name (as it appears on card), and Billing Address. If you prefer, you may FAX the information, or a legible (not too dark) copy of your credit card, to the FAX number listed below.

CONTACT:

E-mail: [email protected] 
cap.columbia.edu
Postal: Center for Applied Probability, ATTENTION: Finance Workshop 
601 CEPSR, Columbia University, Mail code 8906 
530 West 120th Street, New York, NY 10027 
Phone: (212) 854-6096 
FAX: (212) 854-8103

LOCATION:

Warren Hall, Room 107 
Columbia University, New York, NY 
North-east corner of Amsterdam avenue and 115th street (entrance on Amsterdam) 

Organizers:

M. Broadie, P. Glasserman, C. Heyde, S. Kou, and K. Sigman 

For general CAP inquiries: 
[email protected] (Chris Heyde, Director of CAP) 
[email protected] (Karl Sigman, Secretary of CAP)

Friday, November 9th, 2001 
Columbia University, New York City. 
(This web site was updated on November 5, 2001)

This year we will once again have another group of highly distinguished speakers in the usual informal workshop aimed at fostering communication between academia and industry. 

Friday, November 9th, 2001 
Columbia University, New York City. 
(This web site was updated on November 5, 2001)

 

This year we will once again have another group of highly distinguished speakers in the usual informal workshop aimed at fostering communication between academia and industry. 
 

 

SCHEDULE:

Opening Remarks  8:45-9:00

9:00- 9:40        
Philipp Schoenbucher, Bonn University 
"Pricing Exotic Credit Derivatives" based on "A Libor market model with default risk" and "Copula-dependent defaults in intensity models" 

9:40-10:20        
Zhifeng Zhang, Morgan Stanley 
"Simulating Correlated Default Arrival Times and Pricing Basket Default Swaps"

10:20-10:50      
Break

10:50-11:30      
David Chasman, Sempra Energy Trading 
"Managing 'Simple' and Not-So-Simple Energy Risk" 

11:30-12:10      
Keynote Address
Richard Sandor, Environmental Financial Products 

"The Chicago Climate Exchange:  Creating a Market for Greenhouse Gas Emissions Trading"

12:10-1:30
Lunch

1:30-2:10          
Michael Johannes, Columbia Business School 
"The Impact of Jumps in Volatility and Returns"

2:10-2:50
Alan Lewis, OptionCity.net 
"A Simple Option Formula for General Jump-Diffusion and Other Exponential Levy Processes"

2:50-3:30          
Nick Webber, University of Warwick 
"Lattice Methods for Levy Processes"

3:30-4:00
Break

4:00-4:40          
Steve Heston, Goldman Sachs 
"The Expectations Puzzle in a Log-Linear Bond Model"

4:40-5:20          
Phelim Boyle, University of Waterloo 
"Monte Carlo Methods for Asset Allocation"

5:20-6:00          
Wine and cheese reception

REGISTRATION FEES:

Academic: 
By Nov. 2: $110 ($30 student) 
On site: $150 ($40 student)

Corporate: 
By Nov. 2: $220 
On site: $300

A light lunch will be provided, and a wine and cheese reception will be held at the end of the day.

REGISTRATION PROCEDURE:

Send Name, Title, Affiliation, Address and E-mail Address (as we prefer to acknowledge receipt of your registration by e-mail), along with a check or money order payable to CAP to the address below.

Or, to pay by credit card (MC or Visa ONLY), send the same information in an e-mail to the address below and, in addition, include CC#, Exp. Date, Name (as it appears on card), and Billing Address. If you prefer, you may FAX the information, or a legible (not too dark) copy of your credit card, to the FAX number listed below.

CONTACT:

E-mail: [email protected] 
https://cap.columbia.edu
Postal: Center for Applied Probability, ATTENTION: Finance Workshop 
601 CEPSR, Columbia University, Mail code 8906 
530 West 120th Street, New York, NY 10027 
Phone: (212) 854-6096 
FAX: (212) 854-6989

LOCATION:

***Note:  This is a different location from previous years***

L107 Warren Hall 
115th Street and Amsterdam Ave. 
Columbia University, New York City 

Friday, December 1st, 2000 
Columbia University, New York City. 
(This web site was updated on October 20, 2000)

This year we will once again have another group of highly distinguished speakers in the usual informal workshop aimed at fostering communication between academia and industry. There will talks on new markets (credit, energy, and emerging markets) plus recent advances in interest rate models, computational methods, and other topics in mathematical finance. Details of the speakers and the talks will posted soon.

Speakers:

Vladimir Finkelstein--Goldman Sachs 
"Pricing Single Name Credit Derivatives"

Ludger Overbeck--Deutsche Bank AG 
"Credit Portfolio Modeling"

Michael Dempster--Cambridge University 
"Wavelet-Based PDE Methods for Derivative Valuation"

Vadim Linetsky--Northwestern University 
"Eigenfunction Expansion Methods in Derivatives Pricing"

David Heath--Carnegie Mellon 
"Equivalent Martingale Measures and Lévy's Theorem"

Alexander Lipton--Deutsche Bank 
"Pricing and Risk-Managing Exotics on Assets with Stochastic Volatility"

Ronnie Sircar--Princeton University 
"Partial Hedging of Derivative Risk under Stochastic Volatility"

Mikhail Chernov--Columbia University 
"Alternative Models for Stock Price Dynamics" 
 

Organizers:
M. Broadie, P. Glasserman, C. Heyde, S. Kou and K. Sigman 

For general CAP inquiries: 
[email protected] (Chris Heyde, Director of CAP) 
[email protected] (Karl Sigman, Secretary of CAP)

 

1998 Speakers:

  • Kaushik Amin (Lehman Brothers, New York): Emerging Market Derivatives
  • Leif Anderson (General Re Financial Products): Volatility Skews and Extensions of the Libor Market Model
  • Eric Briys (Lehman Brothers, London): Early Default, Absolute Priority Rule Violations and The Pricing of Risky Fixed Rate Debt
  • Alexander Eydeland (Southern Energy): Pricing Power Derivatives
  • Pat Hagan (Banque Paribas): Equivalent Black Volatilities
  • Chris Heyde (Columbia University): Statistical Realities for Financial Time Series
  • Vincent Kaminski (Enron): Value-at-Risk for Portfolios of Energy Derivatives
  • Damien Lamberton (Universite de Marne la Vallee): Random Walk Approximation and Option Prices
  • Bill Morokoff (Goldman Sachs): Applications of the Brownian Bridge to Derivatives Pricing and Risk
  • Art Owen (Stanford University): Safe and Effective Importance Sampling
  • Louis Scott (Morgan Stanley): The Pricing of Default Options and Credit Derivatives
  • L.A.Shepp (Rutgers University): Option Pricing Without Completeness and Non-arbitrage
  • Stuart Turnbull (Queen's University and CIBC): The Intersection Market and Credit Risk

1997 Speakers:

  • O. Cheyette (Barra): Implied Prepayments
  • G. Constantinides (U. of Chicago): Transaction Costs and the Pricing of Derivatives Perspective and Recent Developments
  • F. Delbaen (ETH, Zurich): Arbitrage Theory and Martingale Problems
  • R. Engle (U. of California, San Diego): Time and the Price Impact of a Trade
  • S. Figlewski (New York U.): The Adaptive Mesh Model: A New Approach to Efficient Option Pricing
  • S. Grossman (U. of Pennsylvania, Wharton School): Aspects of Portfolio Insurance
  • F. Jamshidian (Sakura Capital Markets): LIBOR and Swap Market Models and Measures
  • M. Musiela (U. of New South Wales): Exotic Interest Rate Options
  • A. Pelsser (ABN-Amro Bank): Pricing Double Barrier Options using Analytical Inversion of Laplace Transforms"
  • R. Rebonato (Barclays Bank): Correlation, Instantaneous Volatility and the Evolution of the Term Structure of Volatilities in the Pricing of Interest-Rate Options
  • P. Ritchken (Case Western U.): Pricing Options Under Generalized GARCH and Stochastic Volatility Processes
  • Y. Ait Sahalia (U. of Chicago): Nonparametric Risk Management and Implied Risk Aversion
  • J. Sidenius (SimCorp): Examining Multi-factor Market Models

1996 Speakers:

  • P. Bloomfield (Merrill Lynch)
  • P. Carr (Morgan Stanley)
  • J. Detemple (McGill U., Canada)
  • P. Embrechts (ETH, Switzerland)
  • B. Flesaker (Bear Stearns)
  • G.Chichilnisky (Columbia University)
  • H. Leland (U. Calif. Berkeley)
  • A. Lo (MIT)
  • E. Peters (Pan Agora Asset Mgmt)
  • E. Reiner (UBS Securities)
  • S. Ross (Yale U.)
  • W.Segal (Dept. Housing and Urban Development, Washington)
  • S. Shreve (Carnegie Mellon U.)

1995 Speakers:

  • Mark Davis (Mitsubishi Finance): Option hedging and risk-constrained portfolios
  • Emmanuel Derman (Goldman Sachs): Financial Modeling on Wall Street: A Physicist's perspective
  • Raphael Douady (Ecole Normale Superiere and Societe Generale): Infinite dimensional models for the yield curve (Exploiting the smoothness)
  • Hans Fö llmer (Humboldt U.): Different approaches to incompleteness
  • Marco Frittelli (U. Milan, Italy): Valuation principle in security markets models with frictions
  • Paul Glasserman (Columbia U.): Pricing American options by simulation
  • Michael Hieb (UBS Securities): Practical issues in risk management
  • Lane Hughston (Merril Lynch):
  • Dilip Madan (U. Maryland): Estimation of risk neutral and statistical densities using the variance gamma process
  • Antonio Paras (New York U.): Managing the volatility risk of exotic derivatives with vanilla options: uncertain volatility model (UVM)
  • Eckhard Platen (Australian National U.): An attempt to explain the interest rate term structure
  • Wolfgang Runggaldier (U. Padua, Italy): Bond markets when prices are driven by general marked point processes
  • John van der Hoek (U. Adelaide, Australia): Evaluation of American options using a method of lines
  • Paul Wilmott (Oxford U.): Research in mathematical finance at Oxford University
  • Joe Zhou (Bear, Sterns & Co. Inc.): A basic model of commodity price behaviour

1994 Speakers:

  • M. Avellaneda (Courant Institute, New York U.): Valuation and dynamical hedging of derivative securities in the presence of transaction costs: binomial and lognormal models
  • P. Boyle (U. Waterloo, Canada) : Quasi-random Monte Carlo
  • M. Broadie (Columbia U.): American option valuation: new bounds, approximations, and a comparison of existing methods
  • S. Browne (Columbia U.): Optimal investment policies for a firm with a random risk process
  • P. Carr (Cornell U.): Fast accurate valuations of American options
  • D. Heath (Cornell U.): Modeling the random evolution of the term structure of interest rates: the HJM framework
  • R. Mark (Canadian Imperial Bank of Commerce): Risk management
  • A. Mirabelli (Kidder Peabody): Pricing mortgages
  • E. Platen (Australian National U.): Application of stochastic numerical methods in derivative pricing
  • R. Skora (Sumitomo Bank Capital Markets): Measuring credit risk in derivative transactions
  • S. Sundaresan (Columbia U.): Design and valuation of debt contracts
  • J. Traub (Columbia U.): Computational complexity of high dimensional integration with applications to finance
  • W. Willinger (Bellcore): FBM modeling of stock prices and some of the implications for option pricing


For general CAP inquiries: 
[email protected] (Chris Heyde, Director of CAP) 
[email protected] (Karl Sigman, Secretary of CAP)

Other Events

10/11/2013

CONFERENCE "COPULAS AND DEPENDENCE: THEORY AND APPLICATIONS"

Organizers: Victor de la Peña and Lorán Chollete
Co-sponsored by Center for Applied Probability (CAP)

Columbia University's Department of Statistics is organizing a 2-day Conference on Copulas and Dependence Measures. This conference will involve cutting edge research in theoretical developments and applications. The conference is motivated by outstanding challenges in research on dependence, concerning limit theorems for dependence estimation, specification challenges, and high-dimensional data implementation. The conference will also address practical problems of portfolio modeling for banks and regulators. The conference will feature applications in genetics, hydrology and finance. Here is the detailed conference program. Please register if you plan to attend.

Dates: October 11-12, 2013

Location: 303 Mudd, Columbia University

Keynote Speakers: For the conference Keynote and Plenary Talk, we have four internationally renowned researchers including:

Keynote Speakers:

09/23/2011

Workshop on Computational Methods in Applied Sciences

When: September 23 - 25, 2011
Where: Department of Statistics at Columbia University, co-sponsored by the Center for Applied Probability.
Specific location is to be arranged.

Scientific computation has been an important topic in many disciplines. This workshop focuses on the recent advances in efficient computational methods and their applications to applied sciences. Specifically, the topics of the workshop include analyses of Markov chain Monte Carlo, sequential Monte Carlo, particle methods, asymptotic theory and approximations. A list of applications includes astronomy, biology, chemistry, engineering, finance, and social sciences.

05/20/2011

CAP CO-SPONSORED EVENT

"Imaging, Communications and Finance: Stochastic Modeling of Real-world Problems Conference in honor of Lawrence A. Shepp"

June 24-25, 2011

For more information regarding this conference, please go to the link below:

JUNE 15, 2002 (CORNELL UNIVERSITY)

8:00 a.m.              Registration in Room 131, Sage Hall

8:00 a.m.              Shuttle Bus from Holiday Inn to Sage Hall

8:30 a.m.              Shuttle Bus from Holiday Inn to Sage Hall

8:15 – 9:00           Continental Breakfast in the Atrium, Sage Hall

9:00 – 10:30         Presentation in B10, Sage Hall
                             Opening: David Yao, HenkZijm
                             Speakers: Robin Roundy, Wallace Hopp

10:30 – 11:00       Coffee Break in the Atrium

11:00 – 12:30       Presentation in B10
                             Speakers: AviSeidmann, RajanSuri, NicoVandaele

12:30 – 2:00         Lunch Buffet in the Atrium

2:00 – 3:30           Presentation in B10
                             Speakers: HenkZijm, Stanley Gershwin, FikriKaraesmen,

3:30 – 4:00           Coffee Break in the Atrium

4:00 – 5:00           Presentation in B10
                             Speakers: Sridhar Tayur, John Buzacott

5:15                      Shuttle Bus to the Holiday Inn

5:40                      Shuttle Bus to the Holiday Inn

6:00 – 7:00           Cocktail Hour at the Holiday Inn

7:00 – 9:30           Formal Banquet at the Holiday Inn

* Sponsored by the Center for Applied Probability,  Columbia University

 

Abstracts

STRATEGIC CAPACITY PLANNING FOR THE SEMICONDUCTOR INDUSTRY:CURRENT
INDUSTRIAL PRACTICE AND NEW DIRECTIONS

Robin Roundy, MetinCakanyildirim, Woonghee Timothy Huh, Feng Zhang
School of Operations Research and Industrial Engineering
CornellUniversity

We summarize a multi-year research effort designed to provide useful tools for capacity planning decisions in the semiconductor industry.The decisions are crucial and challenging.The business environment is volatile, but equipment has long procurement lead times and is extremely expensive. We will review and evaluate current business practices.We present methods for quantifying the errors in demand forecasts. We present a novel approach for multi-dimensional demand modeling, and discuss practical and algorithmic implications of different stockout cost models.We present efficient algorithms for provably solvable versions of the capacity planning problem.

WORKFORCE AGILITY: MODELS FOR GAINING INSIGHT INTO WHEN AND HOW TO USE CROSS-TRAINING
Wallace J. Hopp
BreedUniversity Professor
Northwestern University

We examine issues that affect the nature of the “best” strategy for cross-training workers in serial production environments.Using a combination of optimization and simulation models, we examine strategies based on chaining, which enable labor capacity to be shared very flexibly.Our results suggest that chaining strategies work robustly well given a suitable task allocation policy and that they offer promise as practical workforce management tools.

Using Transaction Data for the Design of Sequential, Multi-unit, Online Auctions
Abraham Seidmann
SimonGraduateSchool of Business Administration
University of Rochester

Internet auctions for consumers' goods are an increasingly popular selling venue.The Internet's computational ability makes possible the sale of multiple units of the same good in a single auction.We found that many sellers, instead of offering the entire inventory at a single auction, split it into sequential auctions of smaller lots, to reduce the negative market impact of large lots.In the short lecture we plan to show how the available inventory should be split into multiple lots and how many sequential auctions should be run.We also investigate how managers can leverage information technology to improve the design of future auctions.

Assuming a truth-revealing ascending auction model, we quantify the effect of auction lot size on the closing price.We then develop a stochastic optimization model for allocating inventory across multiple auctions.Solving the dynamic programming formulation, we prove that the lot size drops from period to period.The intensity of the decline increases in the holding costs and the website's traffic intensity, while decreasing in the dispersion of consumers' valuations of the good.Finally, we extend this model to dynamically incorporate the results of previous auctions as feedback into the design of consecutive auctions, updating the lot size and number of auctions.We demonstrate how information signals from previous auctions should be used to update the auctioneer's belief s about the customers' valuation distribution, thereby significantly increasing the sellers' profit potential.We conclude the seminar with several practical examples that show the economic benefits of using detailed transaction data for the design of sequential, multi-unit, online auctions and how these benefits are influenced by the inventory holding costs, bid traffic, and the dispersion of consumers' valuations.(Joint research with Professors Pinker and Vakrat.)

RECENT RESULTS ON TWO-MOMENT APPROXIMATIONS, SAFETY LEAD TIMES, AND HYBRID PUSH-PULL SYSTEMS
RajanSuri
Center for Quick Response Manufacturing
University of Wisconsin-Madison

Dr. Buzacott's pioneering works in the areas of modeling job shops, analyzing safety stock and safety lead times, and hybrid material control systems, have inspired many researchers over the years. In this talk we will show some of the latest results in these three areas: (i) simple two-moment approximations for fork-join stations which can be used to model kanban and other material control systems in job shops; (ii) numerical results showing that safety lead times are better than safety stock for multi-product systems over a wide range of parameters; (iii) case studies on implementations of a hybrid push-pull system, called POLCA, at several factories, explaining why the system was chosen and the performance results seen thus far. This talk represents joint work with Ananth Krishnamurthy and Mary Vernon at the University of Wisconsin-Madison.

I-CLIPS : One way to materialize a stochastic model of a manufacturing system
Nico Vandaele
University of Antwerp, Belgium

Building stochastic models that support operational and managerial decision making in manufacturing systems is an intriguing academic research activity. However, transferring these models to industry is even more challenging and it includes not only issues like software development, a dedicated IT-approach and the effective implementation but also a well-thought educational effort. We discuss the software I-CLIPS, which is the materialisation of a multi-product queuing network with embedded lot sizing optimisation. I-CLIPS serves three purposes: better planning, better tuning and better levers for improvement.

Spare Parts Inventory Management at the Royal Netherlands Navy
Dr. W.H.M. Zijm
University of Twente, the Netherlands

In this talk we present models and techniques that have been developed to support the design of a new spare parts management system at the Royal Netherlands Navy. Since we focus on high system availability at ships, failed components or subassemblies are initially replaced by spare items, while the failed items are later repaired and then stored for future re-use. Since military installations on ships often have a complex product structure, and since spare parts are kept in stock both at the ships and at a central facility, we deal with multi-echelon, multi-indenture inventory systems. Our goal is to establishoptimal base stock levels of all components at all sites in order to maximize system availability given limited investment budgets. We extend the analysis to repair shops with limited capacities, each modeled as a BCMP queuing network. In addition, we present results for complex real life systems, indicating that substantial improvements in system availability can be obtained, while at the same time reducing inventory investments with more that 50 %, leading to estimated savings of more than 25 million Euro in inventory investment.

Kanban, CONWIP, PAC, Information Flow, and Multiple Loop Network Decomposition
Stanley B. Gershwin
Department of Mechanical Engineering
Massachusetts Institute of Technology

In many material flow systems (including kanban, CONWIP and PAC), the flow of material is controlled by the presence or absence of tokens. In such systems, a token is generated by the arrival of an order, the arrival of an item of raw material, the departure of a finished item, or by the completion of an operation.The presence of this token is required before some other operation may occur.To generalize, there may be many tokens taking different (but fixed) paths in the system, and the space allowed for the storage of tokens at specific points in the system may be limited.

We describe a class of flow network models which can help the analysis and design of such control mechanisms, and of the manufacturing systems controlled by such mechanisms.Material flows in one part of such a network and tokens flow in the rest of it, but no distinction is made between material and token flow in the analysis.The issuance of a token at the completion of an operation may be viewed as a disassembly, and the requirement that a token be present for an operation to take place may be viewed as an assembly.

These networks are a generalization of more restricted systems that have been analyzed by decomposition methods.In such systems, buffers (links) are finite, machines (nodes) are unreliable, machines may perform assembly and disassembly operations, but the network is limited to acyclic or tree structures.In the larger class, there is no such structural limitation.In particular, there may be multiple loops.

Loops create a new phenomenon that does not exist in acyclic systems: a strong correlation among the quantities in buffers at any time. This is because there is an invariant associated with each loop.(For example, in closed loops where the material visits all the machines and buffers in order, the population is constant.)

We describe a new decomposition method for the performance analysis of these systems.

On the Value of Advance Demand Information in Production/Inventory Systems
FikriKaraesmen
Laboratoire Genie Industriel
EcoleCentrale Paris.

Inspired by the earlier work of Buzacott and Shanthikumar, we investigate the value of advance demand information in production/inventory systems. For a single-stage make-to-stock queue, we assess the value of using advance demand information under a variety of assumptions on the cost of obtaining advance demand lead time, and on the delivery timing requirements. This analysis enables us to identify conditions under which advance demand information may bring significant benefits in capacitated systems. (joint work with G. Liberopoulos and Y. Dallery)

What is Missing to Enable Optimization of Inventory Deployment and Supply Planning?
Sridhar Tayur
GSIA
CarnegieMellonUniversity

Tremendous opportunity exists if we can bridge Top Academic Research and the commercial marketplace. The timing is appropriate because investments in ERP and APS have failed to provide the return, and the practitioners are getting frustrated with existing vendors. Frankly, data is also available at an adequate level. I would like to celebrate John's workshop by showcasing some significant practical contributions that have been made when our community's research has been appropriately applied. This may also lead to a discussion on how to make our research more practically useful in a widespread manner.

The Evolution of Manufacturing System Models: A Personal View
John Buzacott
SchulichSchool of Business
YorkUniversity

This talk outlines the way in which models of manufacturing systems have evolved over the last 50-60 years. It is presented from a personal perspective: how awareness of issues arose and how models developed. The role of direct and indirect industry interactions combined with student originality and commitment will be stressed.  

New York City, USA
Grand Hyatt Hotel
July 25-27 (Wed-Fri), 2001

Sponsored by the INFORMS Applied Probability Society


The Institute for Operations Research and the Management Sciences (INFORMS) Applied Probability Society (APS) will hold its eleventh conference in New York City at the Grand Hyatt Hotel on July 25 - July 27, 2001 (Wednesday-Friday).

The conference is co-sponsored by the Center for Applied probability  (CAP) at Columbia University,  AT&T Laboratories,  and IBM Research.

Pre-registration, hotel information and submission of proposals and abstracts is ONLINE at

The topics of interest include but are not limited to:

  • Markov Processes and Markov Decision Processes
  • Point Processes
  • Particle Systems
  • Stochastic Geometry
  • Stochastic Comparison
  • Stochastic Control and Games
  • Discrete Event Systems
  • Queueing Networks and Stochastic Petri Nets
  • Fluid Models
  • Large Deviations and Extreme Values
  • Financial Engineering
  • E-Commerce
  • Insurance and Financial Models
  • Probabilistic Models in Biology and Medicine
  • Modeling of Computer and Communication Systems
  • Modeling of Manufacturing Systems
  • Modeling of Transportation Systems
  • Inference for Stochastic Models
  • Stochastic Simulation
  • Perturbation Analysis
  • Applications of Stochastic Differential Equations
  • Probabilistic Combinatorial Optimization
  • Probabilistic Analysis of Algorithms
  • Stochastic Scheduling
  • Reliability, Risk and Survival Analysis

Plenary Speakers include

  • John Hull (U. Toronto, Canada. Director, Bonham Centre for Finance),
    author of "Options, Futures and other Derivatives".
  • Tom Leighton (MIT, Akamai.com)
  • Benoit Mandelbrot (Yale U., IBM Research)
  • Ward Whitt (AT&T Labs-Research)

Guidelines for abstract submission:
     
Two kinds of submissions will be accepted:

  1. proposals for organized sessions;
  2. proposals for single papers.

A proposal for an organized session should include one-page abstracts for all presentations (20 minutes each).  A proposal for a paper should include a one-page  abstract.(ONE PRESENTATION PER AUTHOR.)

All submissions will be reviewed by a program committee.  The authors will be notified of the program committee's decision by April 15, 2001.
Deadlines for abstract submission:

  • Feb  1, 2001 - Submission of abstract(s) for single papers and organized sessions.
  • Apr 15, 2001 - Acceptance notification


The session proposals and abstracts should be submitted online 
(this link, if under construction, will be up and running soon)
Organizing Committee:

  • Ed Coffman, Columbia University
  • Chris C. Heyde,  Columbia University
  • Dan Heyman, AT&T Labs
  • Michael Pinedo, New York University
  • Perwez Shahabuddin, Columbia University
  • Larry Shepp, Rutgers University
  • Karl Sigman, Columbia University (Conference Chair)
  • Mark Squillante, IBM Watson Research Center
  • David Yao, Columbia University


Overseas Program Advisors:

  • Asia: Masakiyo Miyazawa (Science University of Tokyo, Japan )
  • Europe: Volker Schmidt (University of Ulm, Germany)
  • Program Committee:
    ​​​​​​​CAP

Questions should be directed to:

Karl Sigman, Chair of the Conference <[email protected]>
and cc'd to <[email protected]> (CAP Administrative Assistant)
 

Thursday, May 4th, 2000
To celebrate Vic's many seminal contributions to Applied Probability, a day-long conference in his honor will be held on May 4, 2000 at Columbia University.  This event will be followed by Applied Probability Day on May 5th. 

Invited speakers include:

  • Alain Bensoussan, 
  • Mark Davis, 
  • Wendell Fleming, 
  • Harold Kushner, 
  • Jin Ma, 
  • Steve Shreve, 
  • Bill Sudderth.

In addition, Sanjoy Mitter and Ray Rishel will comment on Vic's work and on his many contributions.

A dinner in Vic's honor will be held following the conference.

LOCATION:  501 Schermerhorn Hall, Columbia University 
(Enter campus at West 116th Street/Broadway or West 116th 
Street/Amsterdam Avenue.) 

REGISTRATION IS  FREE, but please register. 

For inquiries and registration:

Mrs. Doodmatie Kalicharan, 
Department of Statistics, 
Columbia University, New York, 10027 
Phone : 212-854-3653 
Email : [email protected]

DATE :   Tuesday and Wednesday May 2 and 3, 2000

LOCATION :  55  Broad Street, New York City

INSTRUCTORS: Professors CHRIS HEYDE and STEVE KOU, Columbia University, New York 
 

THE COURSE

Delegates will leave this course with a detailed view of cutting edge developments in model building and statistical inference for pricing models. Enrollment will be restricted to a maximum of 20 delegates to facilitate communication and informal 
discussion.

Professors Heyde and Kou are leading researchers in the area and have brought strong statistical backgrounds and extensive empirical work on real data to bear on modeling problems of finance.

You will learn about:

* building finance models, Classsical models and their extensions to imperfect markets, Model robustness

* semimartingale models with no arbitrage opportunities

* long range dependence, non-semimartingale models and arbitrage opportunities

* quasi-likelihood methods of optimal inference for model characteristics

* heavy versus semi-heavy tailed (log) price distributions

* numerical pricing of exotic options, especially discrete barrier and lookback options

* pricing of interest rate derivatives, including spot rate models, the HJM model, and the market LIBOR model

* jump diffusion models and their closed form solutions for both equity and interest rate derivatives 
 

                                           DAY 1

8.30-9.00am   Registration & Breakfast

9.00-10.30am  Lecture 1 (Heyde). Building stochastic models in finance. Martingales and stochastic calculus.

10.30-11.00am Coffee break and informal discussion

11.00-12.30pm Lecture 2 (Kou). Basic Black-Scholes option Pricing and its extension to imperfect markets.

12.30-1.30pm Lunch (provided)

1.30-3.00pm Lecture 3 (Heyde). Time series methods. Introduction to quasi-likelihood and its applications in finance.

3.00-3.30pm Coffee break and informal discussion

3.30-5.00pm Lecture 4 (Kou). Numerical pricing of continuous and discrete exotic options 
 

                                          DAY 2

8.30-9.00am  Breakfast

9.00-10.30am Lecture 5 (Heyde). More advanced quasi-likelihood. Optimality and precision in estimation.

10.30-11.00am Coffee break and informal discussion

11.00-12.30pm Lecture 6 (Kou). Pricing of interest rate derivatives: spot rate Models, the HJM model, and the market LIBOR model

12.30-1.30pm Lunch (provided)

1.30-3.00pm Lecture 7 (Heyde & Kou) Overview of alternative pricing models (1). Subordinator and stochastic volatility formulations.

3.00-3.30pm Coffee break and informal discussion

3.30-5.00pm Lecture 8 (Heyde & Kou). Overview of alternative pricing models (2). Jump diffusion models and their closed form solutions for both equity and interest rate derivatives. 
  
  

ABOUT THE INSTRUCTORS

PROFESSOR CHRIS HEYDE 
Columbia University

Chris Heyde is Director of the Center for Applied Probability (CAP) and Professor of Statistics at Columbia University. He is Editor-in-Chief of "Journal of Applied Probability" and "Advances in Applied Probability", the premier international journals 
in their area. He has served as President of the Bernoulli Society for Mathematical Statistics and Probability, the theoretical arm of the International Statistical Institute. He is author, or editor, of more than 10 books and more than 180 research 
papers and he has been honored for this research by the awards of the Pitman Medal (1988), Hannan Medal (1994) and Lyle Medal (1995). He is a leading international authority on stochastic modeling and inference and he has recently been focusing on stochastic models in finance. 
 

PROFESSOR STEVE KOU 
Columbia University

Steve Kou is Assistant Professor in the Department of Industrial Engineering and Operations Research at Columbia, where he teaches Financial Engineering. He is a specialist in mathematical finance and is well-known internationally for his research on numerical pricing of discrete exotic options, such as discrete barrier and lookback options; option pricing in imperfect markets; market LIBOR models with jump risk; pricing of electricity options; and jump diffusion models and their closed form solutions for both equity and interest rate derivatives. Some of his results have been widely used in Wall Street, and have been incorporated into standard MBA textbooks, such as the textbook by John Hull. 
  
 

WHO SHOULD ATTEND

This training course is specifically designed for quantitative researchers, financial engineers, analysts, and software developers. Students of financial mathematics will also find it highly beneficial. 
 

COURSE MATERIALS

Each delegate will receive a copy of Professor Heyde's most recent book "Quasi-Likelihood and its Application. A General Approach to Optimal Parameter Estimation", Springer, New York, 1997. Some excerpts from reviews follow:

"The powerful message of this timely book is stated on page 10. "For estimation of parameters in stochastic systems of any kind, it has become increasingly clear that it is possible to replace likelihood-based techniques by quasi-likelihood alternatives, in which only assumptions about means and variances are made in order to obtain estimators. 
There is often little, if any, loss in efficiency..." Chris Heyde has played a major role in the development of QLE. Much of the work in this wonderful book can be traced directly or indirectly to his ideas. We are fortunate that he has added his insight to this authoritative work, which describes a field that has matured to the point that it is now ready to fulfill its promise of becoming a standard tool of statistical analysis." (P.I. Nelson in Journal of the American Statistical Association)

"When reading the book we really understand how deep and effective this approach is when solving diverse inference problems in a very satisfactory way.....In a master style the author demonstrates by example how a particular property can be developed into a general result....The book is written by one of the leading stochasticians of our time." (J. 
Stoyanov in Journal of Applied Mathematics and Stochastic Analysis). 
 

CERTIFICATION

Delegates who complete the two days of instruction will recieve a formal certificate from the Center of Applied Probability of Columbia University recognizing their achievement. 
  
 

                                  CAP TRAINING COURSE

                                   REGISTRATION FORM

                        May 2, 3, 2000 at 55 Broad Street, New York 
 

FIRST NAME:..............................................

FAMILY NAME:............................................

JOB TITLE/POSITION:.....................................

DEPARTMENT:.............................................

COMPANY:...............................................

APPROVING MANAGER:.....................................

ADDRESS:...............................................

.......................................................

CITY/POSTCODE:........................................

TELEPHONE:............................................

FAX:..................................................

EMAIL:................................................ 
  
 

THE REGISTRATION FEE IS: $1500

Your registration fee for the two day course includes Professor Heyde's book together with breakfast, lunch, and morning and afternoon refreshments on both days.

If paying by credit card please complete the details below. Please debit my:

.......Visa, ........Mastercard (tick one)

Card No.:.............................................. 
 

Expiry date:...../...../..... 
 

Account address if different from above:

......................................................

...................................................... 
 

Signature:................................. Date............... 
 

HOW TO BOOK

FAX: (212) 854-6989

EMAIL: [email protected]

To book, fax or email the completed form to CAP to obtain a registration number. You will be given a number, or a waiting list number and, if payment did not accompany the form, a payment due date. If payment is not received by the due date the reservation is forfeited and a space opens up for the next one on the list.

Check should be made payable to 'CAP`.

Postal address: 
    Center for Applied Probability, 
    ATTENTION: Training Course, May 2000, 
    601 CEPSR, 
    Columbia University, Mail Code 8906, 
    530 West 120th Street, New York, 
    NY 10027.

    CAP URL: http://www.cap.columbia.edu/ 
    CAP PHONE: (212) 854-6096

Please note that places are limited to 20 and these will be allocated in order of receipt as indicated above. You are advised to send your payment with this booking form in order to secure a place.

PAYMENT

Payment is required prior to the event. If you require an invoice, please inform us at the time of booking, stating whether you need an original or a fax copy. We accept company checks, made payable to 'CAP`. 
 

CANCELLATION

A refund (less 10% administrative charge) will be made if notification of cancellation is received in writing two full weeks before the course begins. After this date no refunds can be given. A substitute delegate can be admitted at no extra charge. 

A SHORT COURSE BY PROFESSOR WILLIAM D. SUDDERTH, UNIVERSITY OF MINNESOTA

The now classic work "How to Gamble if You Must : Inequalities for Stochastic Processes" by Dubins and Savage (1965) is an elegant, deep and quite general theory of stochastic games. A gambler "controls" the stochastic process of his successive gambles by choosing which games to play and which bets to make. This course will introduce the ideas of Dubins and Savage and also more recent developments in gambling theory such as its application to stochastic games.

Schedule : June 16, 17, 18, 21, 23, 25, 28, 29 and 30, 11:00-12:15pm. Room 622 mathematic Bldg.

For general CAP inquiries: 
[email protected] (Chris Heyde, Director of CAP) 
[email protected] (Karl Sigman, Secretary of CAP)

PROFESSOR C. D. FUH, INSTITUTE OF STATISTICS, TAIWAN
The talks will be based on the following  joint papers by Prof. Fuh and Prof. T. L. Lai at Stanford University :

ASYMPTOTIC EXPANSIONS IN MULTIDIMENSIONAL MARKOV RENEWAL THEORY
We consider a Markov random walk $ \{(X_n,S_n), n \geq 0 \}$ in which $X_n$ takes values in a general state space and $S_n$ takes values in {\bf R}$^d$, and derive an asymptotic expansion for multidimensional Markov renewal theory. The results yield  an asymptotic expansion for the variance of the first passage time $\tau_b= \inf \{n: S_n > b\}$ for $ b>0$, when $S_n$ is a one  dimensional Markov random walk with positive drift. The results are also applied to the asymptotic expansions of stopped  random walks and products of Markov random matrices.

POISSON EQUATION, WALD'S IDENTITIES AND QUICK CONVERGENCE FOR MARKOV RANDOM WALKS
We provide tail probability and moment inequalities, and sufficient conditions for the quick convergence for Markov random walks, without  the assumption of uniform or Harris recurrency for the underlying Markov chain.Our approach is based on the Poisson equation and its associated martingale and Wald equation. We also provide Wald equations for the second moment and a variance formula for Markov random walks.

CORRECTED DIFFUSION APPROXIMATIONS FOR RUIN PROBABILITIES IN MARKOV RANDOM WALKS
Let $(X,S)=\{(X_n, S_n); n \geq 0\}$ be a Markov random walk with finite state space.  For $a \leq 0 <b$ define the stopping times $\tau=\inf\{n:S_n>b\}$ and $T=\inf\{n:S_n \not\in (a,b)\}$.  The diffusion approximations of a one-barrier probability  P\{\tau<\infty|X_0=i\}$, and a two-barrier probability $P\{S_T\geq b|X_0=i\}$ with correction terms are derived. Furthermore, the limiting   distributions of overshoot for a driftless Markov random walk are involved, to approximate the above ruin probabilities.

A NONLINEAR MARKOV RENEWAL THEORY WITH APPLICATIONS TO SEQUENTIAL ANALYSIS
Let $T$ be the first time that a perturbed Markov random walk crosses a nonlinear boundary. One concerns the approximations of the distribution of excess over the boundary, the expected stopping time $E_{\nu} T$, where $E_{\nu}$ denotes the expectation under the Markov chain with initial distribution $\nu$. Applications to sequential analysis of hidden Markov chains and random coefficient autoregression models are given.

Schedule : Tue. June 1st, 11am-12noon, 2pm-3pm, and Wed. June 2nd,  11am-12noon, 2pm-3pm. Location : 301 Mudd Bldg. Please contact Steve Kou for details.

For general CAP inquiries: 
[email protected] (Chris Heyde, Director of CAP) 
[email protected] (Karl Sigman, Secretary of CAP)

This Workshop took place on November 3 - 4, 1995, and focused on the two topics of stability and rare events in the context of stochastic networks. Specific topics of interest included (among other things) multiclass queueing networks; Markov chain stability; connections between performance bounds and stability; stability issues in applications; large deviations theory and applications; network reliability; and Monte Carlo methods. A Springer-Verlag Volume will be published in Summer, 1996 containing a variety of papers from the Workshop. Organizing Committee: S.Browne, P.Glasserman, K.Sigman and D.Yao.

Speakers:

  • V. Anantharam (U. California, Berkeley)

Queues with long-range-dependent arrival processes

  • S. Asmussen (U. Lund, Sweden)

Rare events in the presence of heavy tails

  • D. Bertsimas (MIT)

A new approach to decide stability in fluid multiclass queueing networks: Trajectory decomposition and linear programming

  • H. Chen (U. British Columbia, Canada)

A linear Skorohod problem and its applications

  • J. Dai (Georgia Tech.)

The stability region of two-station queueing networks

  • N. Duffield (AT&T Bell Labs)

Conditional tail asymptotics in large multiplexers

  • P. Glynn (Stanford U.)

Estimation of asymptotic decay rates in queueing models

  • W. Gong (U. Massachusetts, Amherst)

Rational approximation for rare-event probabilities

  • P. Heidelberger (IBM Watson Research Center)

On extending parallelism to serial simulators

  • P.R. Kumar (U. Illinois, Urbana-Champagne)

Uniform functional bounds for multiclass open and closed queueing networks:stability, efficiency performance, and asymptotic loss

  • W. Massey (AT&T Bell Labs)

Strong approximations for time-dependent queues

  • S. Meyn (U. Illinois, Urbana-Champagne)

Stability and optimization of multiclass queueing networks and their fluid models

  • M. Miyazawa (Science U. Tokyo, Japan)

Stability and stochastic bounds for queueing networks with batch movements

  • R. Serfozo (Georgia Tech.)

Markovian network processes with string transitions

  • J. Spencer (Courant Institute, NYU)

Rare event probabilities via an inequality of Svante Janson

  • J. Tsitsiklis (MIT)

Large deviations in certain classes of queueing systems

  • R. Tweedie (Colorado State U.)

Explicit rates of convergence for stochastically monotone Markov chains with applications to a two-server system

  • A. Weiss (AT&T Bell Labs)

Using excess bandwidth in ATM file transfers

  • T. Zajic (IBM Watson Research Center)

Some Examples of the Use of Large Deviations Techniques in Obtaining Asymptotic Information Regarding the Behaviour of Queues with Dependent Input

For information contact:
[email protected]  (Paul Glasserman)
[email protected] (Karl Sigman)
[email protected](David Yao)


For general CAP inquiries: 
[email protected] (Chris Heyde, Director of CAP)
[email protected] (Karl Sigman, Secretary of CAP)