Dynamic programming principle for one kind of stochastic recursive optimal control problem and Hamilton-Jacobi-Bellman equations

Abstract

In this paper, we study one kind of stochastic recursive optimal control problem with the obstacle constraints for the cost function where the cost function is described by the solution of one reflected backward stochastic differential equations. We will give the dynamic programming principle for this kind of optimal control problem and show that the value function is the unique viscosity solution of the obstacle problem for the corresponding Hamilton-Jacobi-Bellman equations.

31 pages

Cited by in corpus (3)

• Probabilistic Interpretation for Systems of Isaacs Equations with Two Reflecting Barriers
• Stochastic Differential Games with Reflection and Related Obstacle Problems for Isaacs Equations
• Optimal Switching of One-Dimensional Reflected BSDEs, and Associated Multi-Dimensional BSDEs with Oblique Reflection