Robust Data-Driven CARA Optimization

40 Pages Posted: 10 May 2021 Last revised: 26 Apr 2024

See all articles by Li Chen

Li Chen

University of Sydney Business School

Arjun Ramachandra

Indian Institute of Management Bangalore

Napat Rujeerapaiboon

National University of Singapore (NUS) - Department of Industrial & Systems Engineering

Melvyn Sim

National University of Singapore (NUS) - NUS Business School

Date Written: May 9, 2021

Abstract

We focus on data-driven, risk-averse optimization problems where decision-makers exhibit constant absolute risk aversion (CARA), represented by an exponential utility function. We consider payoff functions expressible as conic optimization problems, highlighting their expansive use in prescriptive analytics. Aiming to mitigate the overfitting issues inherent in empirical distribution-based optimization, we employ a robust satisficing strategy, which combines a target parameter with a Wasserstein distance metric, to define acceptable solutions, robustly. This target parameter could be determined via cross validation to mitigate overfitting and improve out-of-sample performance. Nevertheless, integrating an exponential utility function into a robust satisficing framework introduces substantial computational challenges. Traditional convex approximations, despite being safe and tractable, do not guarantee feasibility when applied to some appropriate target levels. We overcome this inconsistency by delineating specific conditions, namely, a scenario with complete and bounded recourse, polyhedral uncertainty support and polyhedral metric norm, under which a safe, tractable, and consistent approximation of the data-driven robust satisficing problem can be guaranteed for any reasonably specified target. To ensure compliance with the complete and bounded recourse conditions, we subsequently introduce the notion of augmented exponential utility by restricting the domain of the utility function. We validate our theoretical results with computational experiments in two applications: data-driven portfolio optimization and an optimal location problem. The numerical results underscore the efficacy of incorporating robustness into optimization models, significantly enhancing solution quality as compared to traditional empirical optimization approaches.

Keywords: robust optimization, distributionally robust optimization, conic optimization, exponential utility, robust satisficing

Suggested Citation

Chen, Li and Ramachandra, Arjun and Rujeerapaiboon, Napat and Sim, Melvyn, Robust Data-Driven CARA Optimization (May 9, 2021). Available at SSRN: https://ssrn.com/abstract=3842446 or http://dx.doi.org/10.2139/ssrn.3842446

Li Chen

University of Sydney Business School ( email )

Cnr. of Codrington and Rose Streets
Sydney, NSW 2006
Australia

Arjun Ramachandra

Indian Institute of Management Bangalore ( email )

Bannerghatta Main Road, Bilekahalli
Bengaluru, Karnatak 560076
India

Napat Rujeerapaiboon (Contact Author)

National University of Singapore (NUS) - Department of Industrial & Systems Engineering ( email )

10 Kent Ridge Crescent
Singapore, 115260
Singapore

Melvyn Sim

National University of Singapore (NUS) - NUS Business School ( email )

1 Business Link
Singapore, 117592
Singapore

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