SSD Consistent Criteria and Coherent Risk Measures

The mean-risk approach quantifies the problem of choice among uncertain prospects in a lucid form of only two criteria: the mean, representing the expected outcome, and the risk: a scalar measure of the variability of outcomes. The model is appealing to decision makers but it may lead to inferior conclusions. Several risk measures, however, can be combined with the mean itself into the robust optimization criteria thus generating SSD consistent performances (safety) measures. In this paper we introduce general conditions for risk measures sufficient to provide the SSD consistency of the corresponding safety measures. keywords: decisions under risk, stochastic dominance, mean-risk.