Data-Driven Optimization of Reward-Risk Ratio Measures

Ran Ji () and Miguel Lejeune
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Ran Ji: Department of Systems Engineering and Operations Research, George Mason University, Fairfax, Virginia 22030

INFORMS Journal on Computing, 2021, vol. 33, issue 3, 1120-1137

Abstract: We investigate a class of fractional distributionally robust optimization problems with uncertain probabilities. They consist in the maximization of ambiguous fractional functions representing reward-risk ratios and have a semi-infinite programming epigraphic formulation. We derive a new fully parameterized closed-form to compute a new bound on the size of the Wasserstein ambiguity ball. We design a data-driven reformulation and solution framework. The reformulation phase involves the derivation of the support function of the ambiguity set and the concave conjugate of the ratio function. We design modular bisection algorithms which enjoy the finite convergence property. This class of problems has wide applicability in finance, and we specify new ambiguous portfolio optimization models for the Sharpe and Omega ratios. The computational study shows the applicability and scalability of the framework to solve quickly large, industry-relevant-size problems, which cannot be solved in one day with state-of-the-art mixed-integer nonlinear programming (MINLP) solvers.

Keywords: data-driven optimization; distributionally robust optimization; reward-risk ratio; Wasserstein metric; fractional programming (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:33:y:2021:i:3:p:1120-1137

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