Dynkin game under ambiguity in continuous time

Abstract

In this paper, we want to investigate some kind of Dynkin's game under ambiguity which is represented by Backward Stochastic Differential Equation (shortly BSDE) with standard generator function g(t, y, z). Under regular assumptions, a pair of saddle point can be obtained and the existence of the value function follows. The constrained case is also treated in this paper.