Forward-backward systems for expected utility maximization

TL;DR

This paper introduces a novel approach to utility maximization by reducing the problem to analyzing a coupled Forward-Backward Stochastic Differential Equation, applicable to general utility functions.

Contribution

It develops a new method that connects utility maximization with FBSDEs, broadening the scope beyond specific utility functions.

Findings

Establishes a reduction of utility maximization to FBSDE analysis.

Provides a framework for solving general utility maximization problems.

Enhances understanding of stochastic control via FBSDEs.

Abstract

In this paper we deal with the utility maximization problem with a general utility function. We derive a new approach in which we reduce the utility maximization problem with general utility to the study of a fully-coupled Forward-Backward Stochastic Differential Equation (FBSDE).