Utility maximization via decoupling fields

TL;DR

This paper addresses utility maximization by solving a coupled FBSDE system using decoupling fields, establishing existence and uniqueness for complex, multi-dimensional cases with non-Lipschitz conditions.

Contribution

It introduces the application of decoupling fields to prove existence and uniqueness of solutions for complex utility maximization FBSDEs.

Findings

Proved existence of solutions for the utility maximization FBSDE.

Established uniqueness of solutions under broad conditions.

Extended the method to multi-dimensional, non-Lipschitz systems.

Abstract

We consider the utility maximization problem for a general class of utility functions defined on the real line. We rely on existing results which reduce the problem to a coupled forward-backward stochastic differential equation (FBSDE) and concentrate on showing existence and uniqueness of solution processes to this FBSDE. We use the method of decoupling fields for strongly coupled, multi-dimensional and possibly non-Lipschitz systems as the central technique in conducting the proofs.