Stochastic Recursive Zero-sum Differential Games with Payoff Functional in BDSDEs under Model Uncertainty

Abstract

In this paper, problems related to stochastic recursive 0-sum differential games under model uncertainty are studied. In this model, the cost function is defined by , in which  is the solution of a family of forward and backward doubly stochastic differential equations. We deduced the existence of the saddle points for this robust problem with the selection theorem and comparison theorem of BDSDEs. The specific form of the cost function has also been given.