Qiangjun Tang | Searcharxiv

arXiv2025

Quadratic BSDEs with double constraints driven by G-Brownian motion

In this paper, we investigate the well-posedness of quadratic backward stochastic differential equations driven by G-Brownian motion (referred to as G-BSDEs) with double mean reflections. By employing a representation of the solution via G-BMO martingale techniques, along with fixed point arguments, the Skorokhod problem, the backward Skorokhod problem, and the {\theta}-method, we establish existence and uniqueness results for such G-BSDEs under both bounded and unbounded terminal conditions.

math.PR↗

arXiv2025

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

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.

math.OC↗