Stochastic minimax decision rules for risk of extreme events

Abstract

We use the theory of order statistics, the concepts of first- and second-order stochastic dominance (FSD and SSD) to develop an order statistics SSD minimax decision rule. It can be used to refine choice within the random variables in the SSD noninferior set. We are able to reduce the size of the SSD noninferior set when we assume that the decision-maker is most concerned about the potential adverse outcomes at the right tail of the probability distribution. In other words, we consider the risk of extreme events and build on order statistics in order to refine the decision rules. In some eases, the order statistics SSD minimax decision rule can provide us with a unique choice from among the SSD noninferior set. We define the concept of conditional second-order stochastic dominance (CSSD) in order to model the risk of extreme events. We also use the concept of CSSD to develop a CSSD minimax decision rule.