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. In addition, our paper dedicates in proposing various numerical algorithms to solve for the value function, including finite difference method, Generative Adversarial Networks and Monte Carlo simulation. These methods contribute to the quantitative techniques for solving robust portfolio optimization problems. 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. By testing this robust algorithm on real market data, we show that robust portfolios generally have higher expected utilities and are more stable under strong market downturns.

本文解决了不确定参数下的效用最大化问题。与模型参数在给定范围内自由演化的经典方法相比，我们通过惩罚函数来约束它们。此外，我们的论文致力于提出各种数值算法来求解价值函数，包括有限差分法、生成对抗网络和蒙特卡罗模拟。这些方法有助于解决稳健的投资组合优化问题的定量技术。我们表明，这种稳健的优化过程可以解释为两人零和随机微分博弈。我们证明该值函数满足动态规划原则，并且它是相关的 Hamilton-Jacobi-Bellman-Isaacs 方程的唯一粘度解。