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

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Listed:
  • Yan Wang
  • Aimin Song
  • Cheng-De Zheng
  • Enmin Feng

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.

Suggested Citation

  • Yan Wang & Aimin Song & Cheng-De Zheng & Enmin Feng, 2013. "Nonzero‐Sum Stochastic Differential Game between Controller and Stopper for Jump Diffusions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:761306
    DOI: 10.1155/2013/761306
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    References listed on IDEAS

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    1. Erhan Bayraktar & Virginia Young, 2011. "Proving regularity of the minimal probability of ruin via a game of stopping and control," Finance and Stochastics, Springer, vol. 15(4), pages 785-818, December.
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    Cited by:

    1. Yan Wang & Aimin Song & Enmin Feng, 2014. "Stochastic Maximum Principle for Partial Information Optimal Control Problem of Forward‐Backward Systems Involving Classical and Impulse Controls," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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