The relationship between maximum principle and dynamic programming principle for stochastic recursive optimal control problems and applications to finance

This paper is concerned with the relationship between maximum principle and dynamic programming principle for stochastic recursive optimal control problems. Under the assumption that the value function is enough smooth, we give relations among the adjoint processes, the generalized Hamiltonian function and the value function. An LQ recursive utility portfolio optimization problem in the financial market is discussed to show the applications of our result.