Nonzero-Sum Stochastic Differential Game between Controller and Stopper for Jump Diffusions

Abstract EN

We consider a nonzero-sum stochastic differential game which involves two players, a controller and a stopper.

The controller chooses a control process, and the stopper selects the stopping rule which halts the game.

This game is studied in a jump diffusions setting within Markov control limit.

By a dynamic programming approach, we give a verification theorem in terms of variational inequality-Hamilton-Jacobi-Bellman (VIHJB) equations for the solutions of the game.

Furthermore, we apply the verification theorem to characterize Nash equilibrium of the game in a specific example.