A robust stochastic control problem with applications to monotone mean-variance problems

TL;DR

This paper develops a robust stochastic control framework with a monotone mean-variance cost, utilizing BSDEs with unbounded coefficients, and applies it to portfolio and reinsurance problems, showing equivalence with classical mean-variance control.

Contribution

It introduces a novel approach using BSDEs to solve robust mean-variance control problems with random coefficients, establishing equivalence with traditional models.

Findings

The robust control problem shares the same optimal control as the classical mean-variance problem.

The method applies to portfolio selection and investment-reinsurance problems.

The approach handles unbounded coefficients in the BSDEs.

Abstract

This paper studies a robust stochastic control problem with a monotone mean-variance cost functional and random coefficients. The main technique is to find the saddle point through two backward stochastic differential equations (BSDEs) with unbounded coefficients. We further show that the robust stochastic control problem shares the same optimal control and optimal value with the stochastic control problem with a mean-variance cost functional. The results obtained are then applied to monotone mean-variance and mean-variance portfolio selection problems and monotone mean-variance and mean-variance investment-reinsurance problems.