Robust Utility Maximization with L\'evy Processes

TL;DR

This paper addresses robust portfolio optimization under model uncertainty with Le9vy processes, deriving semi-closed form solutions and analyzing worst-case scenarios for an investor with logarithmic or power utility.

Contribution

It introduces a framework for robust utility maximization considering Le9vy triplets, providing explicit optimal strategies and saddle point analysis for worst-case models.

Findings

Optimal investment strategy exists and is explicitly computed.

Provides a saddle point analysis for worst-case models.

Addresses model uncertainty in jump-diffusion processes.

Abstract

We study a robust portfolio optimization problem under model uncertainty for an investor with logarithmic or power utility. The uncertainty is specified by a set of possible L\'evy triplets; that is, possible instantaneous drift, volatility and jump characteristics of the price process. We show that an optimal investment strategy exists and compute it in semi-closed form. Moreover, we provide a saddle point analysis describing a worst-case model.