Distributionally Robust Reward-risk Ratio Programming with Wasserstein Metric
نویسندگان
چکیده
Reward-risk ratio (RR) is a very important stock market definition. In order to capture the situation that the investor does not have complete information on the distribution of the underlying uncertainty, people extend RR model to distributionally robust reward-risk ratio (DRR) model. In this paper, we study the DRR problem where the ambiguity on the distributions is defined through Wassertein metric. Under some moderate conditions, we show that for a fixed ratio, the DRR problem has the tractable reformulation, which means that we may solve the problem by bisection method. Specifically, we analyze the DRR problems for Sortino-Satchel ratio, Stable Tail Adjusted Return ratio and Omega ratio.
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