On a decomposition result in a Dynkin stopping game

Cloud Makasu y

Department of Mathematics

University of Zimbabwe

P.O. Box 167

Mt. Pleasant, Harare

Zimbabwe

Abstract

In this note we prove that, a two-player, zero-sum Dynkin stopping game connected with a 2-dimensional geometric Brownian motion decomposes into two standard optimal stopping problems with terminal reward costs of the mini and max type respectively, for a given terminal reward cost of the mini-max type, under certain conditions. Our main result supplements and extends the result of Yasuda [18].

Keywords and phrases : Dynkin stopping game, optimal stopping problem, smooth-fit principle.