Stochastic recursive optimal control problem with monotonicity conditions under G-framework

Abstract

In this paper, we study the stochastic recursive optimal control problem under non-Lipschitz settings. More precisely, we suppose that the generator of G-BSDE describing the running cost is uniformly continuous and monotonic with respect to the first unknown variable. Using the comparison theorem for G-BSDE and the stability of viscosity solutions, we establish the dynamic programming principle and the connection between the value function and the viscosity solution of the associated Hamilton-Jacobi-Bellman equation. We provide an example of continuous time Epstein-Zin utility to demonstrate the application of our study.