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

Abstract

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