Utility Maximization in a jump market model

TL;DR

This paper addresses utility maximization in jump market models with compact constraints, deriving a specific BSDE to explicitly characterize the value function and optimal strategies.

Contribution

It introduces a dynamic approach to utility maximization with compact constraints, deriving a unique BSDE and explicit solutions unlike previous convex constraint methods.

Findings

Existence and uniqueness of the BSDE solution are established.

Explicit expression for the value function is provided.

Optimal strategies are characterized explicitly.

Abstract

In this paper, we consider the classical problem of utility maximization in a financial market allowing jumps. Assuming that the constraint set is a compact set, rather than a convex one, we use a dynamic method from which we derive a specific BSDE. We then aim at showing existence and uniqueness results for the introduced BSDE. This allows us to give an explicit expression of the value function and characterize optimal strategies for our problem.