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Near-Optimal Control of Stochastic Recursive Systems Via Viscosity Solution

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  • Liangquan Zhang

    (Beijing University of Posts and Telecommunications)

  • Qing Zhou

    (Beijing University of Posts and Telecommunications)

Abstract

In this paper, we study the near-optimal control for systems governed by forward–backward stochastic differential equations via dynamic programming principle. Since the nonsmoothness is inherent in this field, the viscosity solution approach is employed to investigate the relationships among the value function, the adjoint equations along near-optimal trajectories. Unlike the classical case, the definition of viscosity solution contains a perturbation factor, through which the illusory differentiability conditions on the value function are dispensed properly. Moreover, we establish new relationships between variational equations and adjoint equations. As an application, a kind of stochastic recursive near-optimal control problem is given to illustrate our theoretical results.

Suggested Citation

  • Liangquan Zhang & Qing Zhou, 2018. "Near-Optimal Control of Stochastic Recursive Systems Via Viscosity Solution," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 363-382, August.
    • Handle: RePEc:spr:joptap:v:178:y:2018:i:2:d:10.1007_s10957-018-1300-y
    DOI: 10.1007/s10957-018-1300-y
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    References listed on IDEAS

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    1. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    2. Mokhtar Hafayed & Syed Abbas, 2014. "On Near-Optimal Mean-Field Stochastic Singular Controls: Necessary and Sufficient Conditions for Near-Optimality," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 778-808, March.
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