The accessibility and multiple filtration structure for discrete time multiparameter optimal multiple stopping problems

Abstract

This paper is concerned with the optimal stopping problem for discrete time multiparameter stochastic processes with the index set N^d . The definition of a multiple stopping point and a multiple tactic, and the formulation of a multiple stopping problem for multiparameter stochastic processes are provided. The notion of the accessibility of a multiple stopping point, the conditional qualitative independence and the stability of a multiple multiparameter filtration are introduced. The relation between the accessibility of a multiple stopping point and the structure of a multiple multiparameter filtration, and especially, in the case d = 2, the relation between the predictability of a multiple stopping point and the structure of a multiple multiparameter filtration are explored.

Keywords:

• Optimal stopping
• multiparameter stochastic process
• multiple stopping point
• multiple filtration
• multiple tactic
• accessibility
• conditional qualitative independence
• stability