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Journal of Optimization Theory and Applications

, Volume 178, Issue 2, pp 363–382 | Cite as

Near-Optimal Control of Stochastic Recursive Systems Via Viscosity Solution

  • Liangquan Zhang
  • Qing Zhou
Article
  • 106 Downloads

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 

Mathematics Subject Classification

93E20 49L20 

Notes

Acknowledgements

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).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of ScienceBeijing University of Posts and TelecommunicationsBeijingChina

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