Robust control problems of BSDEs coupled with value functions

TL;DR

This paper addresses robust control problems involving coupled BSDEs and value functions under ambiguity, establishing existence, uniqueness, and applying results to optimal investment with Heston volatility.

Contribution

It introduces a framework for robust control with non-Lipschitz SDEs and coupled BSDEs, including a verification theorem and applications to financial models.

Findings

Proved existence and uniqueness of the value function.

Developed sharp estimations for Heston model with ambiguity.

Applied the theory to optimal investment problems.

Abstract

A robust control problem is considered in this paper, where the controlled stochastic differential equations (SDEs) include ambiguity parameters and their coefficients satisfy non-Lipschitz continuous and non-linear growth conditions, the objective function is expressed as a backward stochastic differential equation (BSDE) with the generator depending on the value function. We establish the existence and uniqueness of the value function in a proper space and provide a verification theorem. Moreover, we apply the results to solve two typical optimal investment problems in the market with ambiguity, one of which is with Heston stochastic volatility model. In particular, we establish some sharp estimations for Heston model with ambiguity parameters.