Data-Driven Optimization of Reward-Risk Ratio Measures

36 Pages Posted: 23 Dec 2015 Last revised: 23 Feb 2020

See all articles by Ran Ji

Ran Ji

George Mason University

Miguel Lejeune

George Washington University

Date Written: Feb 20, 2020

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 MINLP solvers.

Keywords: Data-Driven Optimization, Distributionally Robust Optimization, Reward-Risk Ratio, Risk-Adjusted Return Financial Measure, Wasserstein Metric, Ambiguous Expectation Constraint

Suggested Citation

Ji, Ran and Lejeune, Miguel, Data-Driven Optimization of Reward-Risk Ratio Measures (Feb 20, 2020). Available at SSRN: https://ssrn.com/abstract=2707122 or http://dx.doi.org/10.2139/ssrn.2707122

Ran Ji

George Mason University ( email )

Fairfax, VA
United States

Miguel Lejeune (Contact Author)

George Washington University ( email )

Washington, DC 20052
United States

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