Near-Optimal Control of Stochastic Recursive Systems Via Viscosity Solution
- 79 Downloads
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.
KeywordsDynamic programming principle Forward–backward stochastic differential equations Near-optimal control Super-/subdifferentials
Mathematics Subject Classification93E20 49L20
The authors wish to thank the editor and the referees for their valuable comments and constructive suggestions which improved the presentation of this manuscript. We also thank Dr. J. Yang for her careful reading and suggestions. L. Zhang acknowledges the financial support partly by the National Nature Science Foundation of China (Nos. 11701040, 11471051 and 11371362) and Innovation Foundation of BUPT for Youth (No. 500417024). Q. Zhou acknowledges the financial support partly by the National Nature Science Foundation of China (Nos. 11471051 and 11371362).
- 1.Bismut, J.M.: Théorie Probabiliste du Contrôle des Diffusions. Memoirs of the American Mathematical Society, 176, Providence, Rhode Island (1973)Google Scholar
- 28.Tang, M.N.: Stochastic maximum principle of near-optimal control of fully coupled forward–backward stochastic differential equation. In: Abstract and Applied Analysis 2014, 12 (2014). https://doi.org/10.1155/2014/361259
- 29.Nie, T.Y., Shi, J.T., Wu Z.: Connection between MP and DPP for stochastic recursive optimal control problems: viscosity solution framework in local case. In: Proceedings of 2016 American Control Conference, pp. 7225–7230, July 6–8, Boston (2016)Google Scholar