Dynkin game under ambiguity in continuous time

TL;DR

This paper studies a continuous-time Dynkin game under ambiguity modeled by BSDEs, establishing saddle points and value functions under regular assumptions, including constrained cases.

Contribution

It introduces a framework for Dynkin games under ambiguity using BSDEs and proves the existence of saddle points and value functions, extending to constrained scenarios.

Findings

Existence of saddle points under regular assumptions.

Value function exists for the game.

Extension to constrained cases.

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.