Forward Backward SDEs Systems for Utility Maximization in Jump Diffusion Models

TL;DR

This paper develops a framework using forward-backward stochastic differential equations to solve utility maximization problems in jump-diffusion financial models, providing explicit solutions for certain cases.

Contribution

It introduces a novel approach to utility maximization via forward-backward SDE systems in jump models, extending previous methods to include explicit solutions for specific utilities.

Findings

Explicit solutions for pure jump models

Optimal strategies expressed via implicit forward-backward systems

Applicability to exponential utility functions

Abstract

We consider the classical problem of maximizing the expected utility of terminal net wealth with a final random liability in a simple jump-diffusion model. In the spirit of Horst et al. (2014) and Santacroce-Trivellato (2014), under suitable conditions the optimal strategy is expressed in implicit form in terms of a forward backward system of equations. Some explicit results are presented for the pure jump model and for exponential utilities.