Baxter-Chacon topology and optimality for multivariate multiple stopping problems

Abstract

This paper is concerned with optimal stopping problems for discrete time stochastic processes with the multiple stopping rules, which are also called multivariate stopping problems or cooperative stopping problems. The compactness of the set of all randomized multiple stopping rules in the Baxter-Chacon topology is proved. Then it is applied to prove the existence theorems of optimal multivariate multiple stopping problems for Banach-valued stochastic processes.

Keywords:

• Baxter-Chacon topology
• optimal multivariate stopping
• multiple stopping
• randomized multiple stopping