Robust utility maximization with nonlinear continuous semimartingales

2022/06/28 by David Criens, Criens, David, Lars Niemann +1
Decision Sciences · Economics, Econometrics and Finance · #60G65 #91B16 #93E20 #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Market Dynamics and Volatility #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Probability (math.PR) #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.2206.14015

openalex publication_date 2022/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study a robust utility maximization problem in continuous time under model uncertainty. The model uncertainty is governed by a continuous semimartingale with uncertain local characteristics. Here, the differential characteristics are prescribed by a set-valued function that depends on time and path. We show that the robust utility maximization problem is in duality with a conjugate problem, and we study the existence of optimal portfolios for logarithmic, exponential and power utilities.

Related

• Robust Utility Maximization with Drift and Volatility Uncertainty
• Robust Utility Maximization with Lévy Processes
• The Stability of the Constrained Utility Maximization Problem - A BSDE Approach
• Optimal investment and consumption under logarithmic utility and uncertainty model
• Robust Utility Maximizing Strategies under Model Uncertainty and their Convergence