Data-Driven Optimization of Reward-Risk Ratio Measures
Ran Ji (rji2gmu.edu)
Abstract: We investigate a class of distributionally robust optimization problems that have direct applications in finance. They are semi-infinite programming problems with ambiguous expectation constraints in which fractional functions represent reward-risk ratios. We use the Wasserstein metric to model ambiguity and 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, and yields a mathematical programming problem in a finite dimensional constraint space. We design modular bisection algorithms with finite convergence property. We specify new ambiguous portfolio optimization models for the Sharpe, Sortino, Sortino-Satchel, and Omega ratios. The computational study shows the applicability and scalability of the framework to solve large, industry-relevant size problems.
Keywords: Data-Driven Optimization, Distributionally Robust Optimization, Reward-Risk Ratio, Risk-Adjusted Return Financial Measure, Wasserstein Metric, Ambiguous Expectation Constraint
Category 1: Stochastic Programming
Category 2: Applications -- OR and Management Sciences (Finance and Economics )
Citation: Working Paper under submission.
Entry Submitted: 01/16/2017
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