Baxter-Chacon topology and optimality for multivariate multiple stopping of two-parameter stochastic processes

Abstract

This paper is concerned with the optimal multiple stopping problems for discrete time two-parameter stochastic processes under the conditional qualitative independence on the underlying filtration. The objective function studied here is the functional of the expected value when stopping at multiple random points, and the optimal multiple stopping problem in this case is also called a multivariate multiple stopping problem or a cooperative multiple stopping problem. The compactness of the set of all randomized multiple stopping points in the Baxter-Chacon topology is proved. Then it is applied in order to prove the existence theorems of optimal multivariate multiple stopping problems for Banach-valued two-parameter stochastic processes.