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

Yan Wang, Aimin Song, Cheng- De Zheng and Enmin Feng

Abstract and Applied Analysis, 2013, vol. 2013, 1-7

Abstract:

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:761306

DOI: 10.1155/2013/761306

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