A Direct Approach to the Solution of Optimal Multiple-Stopping Problems

Abstract

The issue of making a decision several times and thereby earning a reward is the focus of this chapter. It considers the problem of multiply stopping a general one-dimensional diffusion process with fairly general reward functions at each decision time. A key aspect of the problem is the requirement that succeeding decisions be delayed by at least the length of time of a refraction period following a preceding decision. Using a conditioning argument, the multiple-stopping problem can be solved using an iterative set of single-stopping problems for which several solution approaches are known. The refraction period adds an interesting twist to the problem. A tractable solution method is developed for those processes whose distributions are known. This work is motivated by the recent paper [Carmona and Dayanik (Math Oper Res 32:446–460, 2008)].

It is with great pleasure that we contribute a paper to this Festschrift in honor of Onésimo Hernández-Lerma’s 65th birthday. He has made many contributions to the stochastic control of Markov processes literature; our interests have many intersections with his work. This contribution honors his career at this important milestone and is dedicated to him.