G-BSDEs with non-Lipschitz coefficients and the corresponding stochastic recursive optimal control problem
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.
Cite
@article{arxiv.2508.17731,
title = {G-BSDEs with non-Lipschitz coefficients and the corresponding stochastic recursive optimal control problem},
author = {Wei He and Qiangjun Tang},
journal= {arXiv preprint arXiv:2508.17731},
year = {2026}
}
Comments
We have discovered that the existence and uniqueness of solutions to G-BSDE under monotonicity conditions have already been established (see DOI:10.16205/j.cnki.cama.2019.0015). We apologize sincerely for the insufficiently comprehensive literature review conducted earlier