# Robust utility maximization under model uncertainty via a penalization approach

arXiv: https://arxiv.org/abs/1907.13345 · HTML: https://mlsanity.com/paper/1907.13345/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jul 2019.

## Built on by (most cited first, 1 of 1)

- [Markov Decision Processes under Model Uncertainty](https://mlsanity.com/paper/2206.06109/) (2022)

## Abstract (arXiv)

This paper addresses the problem of utility maximization under uncertain parameters. In contrast with the classical approach, where the parameters of the model evolve freely within a given range, we constrain them via a penalty function. We show that this robust optimization process can be interpreted as a two-player zero-sum stochastic differential game. We prove that the value function satisfies the Dynamic Programming Principle and that it is the unique viscosity solution of an associated Hamilton-Jacobi-Bellman-Isaacs equation. We test this robust algorithm on real market data. The results show that robust portfolios generally have higher expected utilities and are more stable under strong market downturns. To solve for the value function, we derive an analytical solution in the logarithmic utility case and obtain accurate numerical approximations in the general case by three methods: finite difference method, Monte Carlo simulation, and Generative Adversarial Networks.