Stochastic recursive optimal control problem of reflected stochastic differential systems

ABSTRACT

In this paper, we study one kind of stochastic recursive optimal control problem in which the control system is stochastic differential equations reflected in a domain and the cost functional is defined by generalised backward stochastic differential equations with reflection. We establish the dynamic programming principle for the value function and show that it is a viscosity solution of the associated obstacle problem for the corresponding Hamilton-Jacobi-Bellman equation with a nonlinear Neumann boundary condition.

KEYWORDS:

• Stochastic recursive optimal control
• generalised reflected backward stochastic differential equations
• dynamic programming principle
• viscosity solution
• nonlinear Neumann boundary condition

AMS 2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 93E20
• 60H99
• 60H30
• 35K86

Acknowledgments

The author is grateful to the anonymous referees for very helpful comments and suggestions on the original version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work is partially supported by the National Natural Science Foundation of China (Grant No. 11601280 and 11601282).