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Maximum Principle for Stochastic Recursive Optimal Control Problems Involving Impulse Controls

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  • Zhen Wu
  • Feng Zhang

Abstract

We consider a stochastic recursive optimal control problem in which the control variable has two components: the regular control and the impulse control. The control variable does not enter the diffusion coefficient, and the domain of the regular controls is not necessarily convex. We establish necessary optimality conditions, of the Pontryagin maximum principle type, for this stochastic optimal control problem. Sufficient optimality conditions are also given. The optimal control is obtained for an example of linear quadratic optimization problem to illustrate the applications of the theoretical results.

Suggested Citation

  • Zhen Wu & Feng Zhang, 2012. "Maximum Principle for Stochastic Recursive Optimal Control Problems Involving Impulse Controls," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:709682
    DOI: 10.1155/2012/709682
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    References listed on IDEAS

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    1. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    2. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
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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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