Friday, February 2, 2007
02:30 PM in BRNG 1222
Professor Peter Bank
Department of Statistics, Columbia University

American Options and the Multi-Armed Bandit: Applications of a Stochastic Representation Theorem

Abstract

We shall discuss some recent approaches to optimal stopping problems and to dynamnic allocation problems of the multi-armed bandit type. Both of these optimization problems turn out to be intimately related to the problem of writing a given stochastic process as an integral over a running supremum of another process. For the optimal stopping problem of American options, this process provides a universal exercise signal which works for all puts on a common underlying. For dynamic allocation problems, it yields the Gittins' celebrated performance index and allows us to completely characterize optimal allocation strategies as index policies.