A Direct Approach to the Solution of Optimal Multiple-Stopping Problems
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)].
KeywordsPayoff Function Decision Time Swing Option Smooth Pasting Conditioning Argument
The research of Richard H. Stockbridge was supported in part by the U.S. National Security Agency under Grant Agreement Number H98230-09-1-0002. The United States Government is authorized to reproduce and distribute reprints notwithstanding any copyright notation herein. The research of Chao Zhu was supported in part by a grant from the UWM Research Growth Initiative and under NSF grant DMS-1108782.
- 12.M. Kobylanski, M-C Quenez and E. Rouy-Mironescu, Optimal multiple stopping time problems, Ann. Appl. Probab., 21 (2011), 1365–1399.Google Scholar
- 14.M. Villinski, A methodology for valuing multipe-exercise option contracts for water Center for International Food and Agricultural Policy Working Paper WP-03-4.Google Scholar