Robust Optimization with Moment-Dispersion Ambiguity

68 Pages Posted: 2 Aug 2023 Last revised: 30 Aug 2024

See all articles by Li Chen

Li Chen

University of Sydney Business School

Chenyi Fu

School of Management, Northwestern Polytechnical University

Fan Si

National University of Singapore (NUS) - NUS Business School

Melvyn Sim

National University of Singapore (NUS) - NUS Business School

Peng Xiong

National University of Singapore (NUS) - NUS Business School

Date Written: July 29, 2023

Abstract

Robust optimization presents a compelling methodology for optimization under uncertainty, providing a practical, ambiguity-averse evaluation of risk when the probability distribution is encapsulated by an ambiguity set. We introduce the moment-dispersion ambiguity set, an improvement on the moment-based set, enabling separate characterization of a random variable's location, dispersion, and support. To describe dispersion, we define the dispersion characteristic function, capturing complex attributes like sub-Gaussian and asymmetric dispersion, and its associated dispersion characteristic set, which serves as the input format for representing dispersion ambiguity in algebraic modeling tools. We devise a process for constructing and integrating ambiguity sets, showcasing their modeling flexibility. In particular, we introduce the independence propensity hyper-parameter to foster joint ambiguity set creation for multiple random variables, enhancing our model's real-world applicability and facilitating varying interdependence characterization without needing a correlation matrix. For ambiguous risk assessment over moment-dispersion ambiguity sets, we develop safe tractable approximations for assessing entropic risks linked with affine and convex piecewise affine cost functions, accommodating varying risk tolerances. Lastly, we demonstrate the superior numerical performance of our model over other robust optimization models by adjusting the independence propensity hyper-parameter when limited to marginal information. In data-driven experiments, we find that the moment-dispersion ambiguity sets yield less conservative decisions than classic moment-based sets and more robust decisions than Wasserstein ambiguity sets in data-limited scenarios.

Keywords: robust optimization, ambiguity set, exponential conic optimization History : May 29, 2024

JEL Classification: C61

Suggested Citation

Chen, Li and Fu, Chenyi and Si, Fan and Sim, Melvyn and Xiong, Peng, Robust Optimization with Moment-Dispersion Ambiguity (July 29, 2023). Available at SSRN: https://ssrn.com/abstract=4525224 or http://dx.doi.org/10.2139/ssrn.4525224

Li Chen

University of Sydney Business School ( email )

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

Chenyi Fu (Contact Author)

School of Management, Northwestern Polytechnical University ( email )

27 West Youyi Road, Beilin District, Xi'an Shaanxi
Xi'an, Shaanxi 710072
China

Fan Si

National University of Singapore (NUS) - NUS Business School

Melvyn Sim

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

1 Business Link
Singapore, 117592
Singapore

Peng Xiong

National University of Singapore (NUS) - NUS Business School

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