Robust Data-Driven CARA Optimization

Abstract

Inspired by Von Neumann's foundational work on expected utility, this paper extends the data-driven expected utility maximization framework under constant absolute risk aversion (CARA) preferences by incorporating nonlinear payoff functions and enhancing robustness. These improvements aim to broaden the applicability of utility maximization in prescriptive analytics and to improve out-of-sample performance, particularly in data-scarce settings, respectively. The combined nonlinearity of exponential utility and payoff functions presents significant computational challenges in ensuring robustness. We show that existing safe tractable approximation techniques are overly conservative, potentially causing unexpected infeasibility. To address this, we define a notion of consistent approximation and propose an augmentation technique that provably retains the consistency in the approximation. Theoretical insights are validated through computational experiments in two applications: data-driven portfolio optimization and facility location optimization. Our results demonstrate the effectiveness of incorporating robustness into prescriptive analytics, yielding solutions that significantly outperform traditional empirical and stochastic optimization. Our utility maximization framework is therefore not only robust, but also interpretable, scalable, and adaptable to a wide variety of real-world risk-aware decision-making problems involving nonlinear payoffs.

Keywords: Data-driven robust optimization, Exponential utility, Conic optimization