Dynkin game under g-expectation in continuous time

Abstract

AbstractIn this paper, we investigate some kind of Dynkin game under g-expectation induced by backward stochastic differential equation (short for BSDE). The lower and upper value functions $$\underline{V}_t=ess\sup \nolimits _{\tau \in {\mathcal {T}_t}} ess\inf \nolimits _{\sigma \in {\mathcal {T}_t}}\mathcal {E}^g_t[R(\tau ,\sigma )]$$ V ̲ t = e s s sup τ ∈ T t e s s inf σ ∈ T t E t g [ R ( τ , σ ) ] and $$\overline{V}_t=ess\inf \nolimits _{\sigma \in {\mathcal {T}_t}} ess\sup \nolimits _{\tau \in {\mathcal {T}_t}}\mathcal {E}^g_t[R(\tau ,\sigma )]$$ V ¯ t = e s s inf σ ∈ T t e s s sup τ ∈ T t E t g [ R ( τ , σ ) ] are defined, respectively. Under some suitable assumptions, a pair of saddle points is obtained and the value function of Dynkin game $$V(t)=\underline{V}_t=\overline{V}_t$$ V ( t ) = V ̲ t = V ¯ t follows. Furthermore, we also consider the constrained case of Dynkin game.