DYNAMIC PROGRAMMING PRINCIPLE FOR ONE KIND OF STOCHASTIC RECURSIVE OPTIMAL CONTROL PROBLEM WITH MARKOVIAN SWITCHING

In this paper, we study one kind of stochastic recursive optimal control problem with Markovian Switching. In this problem, the cost functional is described by the solution of backward stochastic differential equations with Markov chains. We prove the dynamic programming principle for this kind of optimal control problem and show that the value function is the unique viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation.