Class09

Rare-event simulation methodology for stochastic systems with heavy-tailed characteristics has been of significant interest to the operations research / discrete-event simulation communities in recent years. Heavy-tailed characteristics arise often in standard models utilized in various applied settings such as computational finance, insurance risk and queueing.

In this talk, we shall present an efficient importance sampling algorithm for computing tail probabilities associated to the maximum of a random walk with negative drift and heavy-tailed increments. This algorithm provides solution to an important open problem in the context of rare-event simulation for systems with heavy-tailed characteristics. In order to show efficiency of our algorithm we develop new techniques based on Lyapunov bounds that can be applied to quantify the efficiency of a given importance sampling algorithm for general first passage time Markov chain problems.

After discussing some motivating applications in various settings such as insurance and queueing, we will review a precise and widely used mathematical description of efficiency in the context of rare-event simulation as well as classical results involving efficient importance sampling schemes. Finally, we shall present our efficient simulation algorithm for the tail of the maximum of a random walk with heavy-tailed increments and will discuss the mathematical justification of its efficiency. (This is joint work with Peter Glynn).

Jose H. Blanchet joined the Department of Statistics at Harvard University in 2004 as an Assistant Professor. Jose holds a M.Sc. in Engineering-Economic Systems and Operations Research and a Ph.D. in Management Science and Engineering, both from Stanford University. Jose also holds two B.Sc. degrees: one in Actuarial Science and another one in Applied Mathematics from ITAM (Mexico). Prior to joining Stanford, Jose worked for two years as an analyst in Protego Financial Advisors, a leading investment bank in Mexico. Jose has research interests in applied probability, computational finance, performance engineering, queueing theory, risk management, rare-event analysis, stochastic modeling, and simulation.

Host: Prof. Vakili
Student Host: Kirk Wesselowski