G-BSDEs with non-Lipschitz coefficients and the corresponding stochastic recursive optimal control problem

TL;DR

This paper investigates the existence and uniqueness of solutions for non-Lipschitz G-BSDEs and explores their connection to stochastic recursive optimal control problems, employing comparison theorems and viscosity solutions.

Contribution

It extends the theory of G-BSDEs to non-Lipschitz generators and links these to stochastic control via the dynamic programming principle and HJB equations.

Findings

Established existence and uniqueness for non-Lipschitz G-BSDEs.

Proved the dynamic programming principle for the control problem.

Connected the value function with viscosity solutions of HJB equations.

Abstract

In this paper, we study the existence and uniqueness of solutions to a class of non-Lipschitz G-BSDEs and the corresponding stochastic recursive optimal control problem. More precisely, we suppose that the generator of G-BSDE 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.