Near-Optimal Control of Stochastic Recursive Systems Via Viscosity Solution

Liangquan Zhang () and Qing Zhou ()
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Liangquan Zhang: Beijing University of Posts and Telecommunications
Qing Zhou: Beijing University of Posts and Telecommunications

Journal of Optimization Theory and Applications, 2018, vol. 178, issue 2, No 3, 363-382

Abstract: 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.

Keywords: Dynamic programming principle; Forward–backward stochastic differential equations; Near-optimal control; Super-/subdifferentials; 93E20; 49L20 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-018-1300-y

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