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.
"Nonzero-Sum Stochastic Differential Game between Controller and Stopper for Jump Diffusions." Abstr. Appl. Anal. 2013 (SI23) 1 - 7, 2013. https://doi.org/10.1155/2013/761306