## Abstract and Applied Analysis

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

#### 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 761306, 7 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393450463

Digital Object Identifier
doi:10.1155/2013/761306

Mathematical Reviews number (MathSciNet)
MR3055963

Zentralblatt MATH identifier
1272.91029

#### Citation

Wang, Yan; Song, Aimin; Zheng, Cheng-De; Feng, Enmin. Nonzero-Sum Stochastic Differential Game between Controller and Stopper for Jump Diffusions. Abstr. Appl. Anal. 2013, Special Issue (2012), Article ID 761306, 7 pages. doi:10.1155/2013/761306. https://projecteuclid.org/euclid.aaa/1393450463

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