Modifications of the Omega ratio for decision making under uncertainty

Abstract

The Omega ratio (Ω-ratio) was proposed by Shadwick and Keating in 2002 as a performance measure applied to rankings of assets, portfolios or funds. It involves partitioning returns into loss and gain below and above a given threshold. The original version was designed for decision making under risk (probabilities completely known), but recent research has shown that this measure can be adapted to decision making
under partial information (likelihood known incompletely). Our contribution will be to use the concept of the Omega ratio in decision making under uncertainty (DMUU) which occurs when the decision maker (DM) chooses the appropriate alternative on the basis of certain scenarios for which probabilities are not known at all. The goal of this article is to adjust the Ω-ratio to DMUU so that it takes into consideration the DM’s attitude towards risk and the distribution of all payoffs connected with particular decisions. The Ω-ratio is combined with a hybrid of Hurwicz and Bayes rules proposed by the author in another paper. The significant advantage of the new measure, Ω(H+B)ratio, is the possibility to compare alternatives (strategies, projects) when the likelihood of particular scenarios is not known or when the DM does not intend to use the available data.