Triangular function and continuity property of multiparameter optimal stopping value

摘要

This paper is concerned with the optimal stopping problem for discrete time multiparameter stochastic processes with the index set N~d. A generalization of Elton's results for one-parameter optimal stopping problems to the case of multiparameter optimal stopping problems is given. The optimal stopping value of a discrete time multiparameter independent uniformly integrable stochastic process is continuous for the topology of convergence in distribution.