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The Optimal Control Problem with State Constraints for Fully Coupled Forward‐Backward Stochastic Systems with Jumps

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  • Qingmeng Wei

Abstract

We focus on the fully coupled forward‐backward stochastic differential equations with jumps and investigate the associated stochastic optimal control problem (with the nonconvex control and the convex state constraint) along with stochastic maximum principle. To derive the necessary condition (i.e., stochastic maximum principle) for the optimal control, first we transform the fully coupled forward‐backward stochastic control system into a fully coupled backward one; then, by using the terminal perturbation method, we obtain the stochastic maximum principle. Finally, we study a linear quadratic model.

Suggested Citation

  • Qingmeng Wei, 2014. "The Optimal Control Problem with State Constraints for Fully Coupled Forward‐Backward Stochastic Systems with Jumps," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:216053
    DOI: 10.1155/2014/216053
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    References listed on IDEAS

    as
    1. Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.
    2. Epstein, Larry G. & Ji, Shaolin, 2014. "Ambiguous volatility, possibility and utility in continuous time," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 269-282.
    3. Jingtao Shi, 2012. "Necessary Conditions for Optimal Control of Forward-Backward Stochastic Systems with Random Jumps," International Journal of Stochastic Analysis, Hindawi, vol. 2012, pages 1-50, April.
    4. Shaolin Ji & Qingmeng Wei & Xiumin Zhang, 2012. "A Maximum Principle for Controlled Time-Symmetric Forward-Backward Doubly Stochastic Differential Equation with Initial-Terminal Sate Constraints," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-29, December.
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