Contribution to the optimal stopping problem

Abstract

We consider the optimal stopping problem for a Markov chain X(n), n=0, 1, ... and a payoff function f(n, x). We establish effective numerical methods to calculate the value — i.e. the supremum over all finite stopping times T of E(f (T,X(T)). We analyze in detail the well known Sn/n problem and give numerical answers to the following problem: in tossing a coin what is the maximum expected fraction of heads obtainable under optimal stopping?