标题： 带有非Lipschitz系数的G-BSDEs及其相应的随机递归最优控制问题 显示英文标题

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

摘要： 在本文中，我们研究一类非Lipschitz G-BSDE解的存在性和唯一性以及相应的随机递归最优控制问题。更精确地说，我们假设G-BSDE的生成器关于第一个未知变量是均匀连续且单调的。利用G-BSDE的比较定理和粘性解的稳定性，我们建立了动态规划原理，并建立了价值函数与相关哈密顿-雅可比-贝尔曼方程的粘性解之间的联系。我们提供了一个连续时间Epstein-Zin效用的例子来展示我们研究的应用。 显示英文摘要

摘要： 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.