Risk-sensitive Dynkin games with heterogeneous Poisson random intervention times

TL;DR

This paper extends the theory of Dynkin games by incorporating risk-sensitive criteria and heterogeneous Poisson intervention times, connecting them to stochastic differential games using Krylov's randomized stopping technique.

Contribution

It generalizes previous models to include risk sensitivity and different intervention times, and links these games to stochastic differential games.

Findings

Established existence of solutions for risk-sensitive Dynkin games with heterogeneous intervention times.

Connected constrained risk-sensitive Dynkin games to stochastic differential games.

Extended the framework to include risk-sensitive criteria and independent Poisson intervention times.

Abstract

The paper solves constrained Dynkin games with risk-sensitive criteria, where two players are allowed to stop at two independent Poisson random intervention times, via the theory of backward stochastic differential equations. This generalizes the previous work of [Liang and Sun, Dynkin games with Poisson random intervention times, SIAM Journal on Control and Optimization, 2019] from the risk-neutral criteria and common signal times for both players to the risk-sensitive criteria and two heterogenous signal times. Furthermore, the paper establishes a connection of such constrained risk-sensitive Dynkin games with a class of stochastic differential games via Krylov's randomized stopping technique.