Power Utility Maximization in Constrained Exponential L\'evy Models

TL;DR

This paper develops explicit solutions for power utility maximization in constrained exponential Lévy models, using a novel transformation to simplify the Bellman equation and analyze optimal investment strategies.

Contribution

It introduces a new method to solve the utility maximization problem explicitly under convex constraints by transforming the model and avoiding technical assumptions.

Findings

Explicit solutions derived for convex constraints

Transformation simplifies the Bellman equation

Discussion of implications for q-optimal martingale measures

Abstract

We study power utility maximization for exponential L\'evy models with portfolio constraints, where utility is obtained from consumption and/or terminal wealth. For convex constraints, an explicit solution in terms of the L\'evy triplet is constructed under minimal assumptions by solving the Bellman equation. We use a novel transformation of the model to avoid technical conditions. The consequences for q-optimal martingale measures are discussed as well as extensions to non-convex constraints.