Stochastic minimax decision rules for risk of extreme events

We use the theory of order statistics, the concepts of first- and second-or der stochastic dominance (FSD and SSD) to develop an order statistics SSD m inimax decision rule. It can be used to refine choice within the random var iables in the SSD noninferior set. We are able to reduce the size of the SS D noninferior set when we assume that the decisionmaker is most concerned a bout the potential adverse outcomes at the right tail of the probability di stribution. In other words, we consider the risk of extreme events and buil d on order statistics in order to refine the decision rules. In some cases, the order statistics SSD minimax decision rule can provide us with a uniqu e choice from among the SSD noninferior set. We define the concept of condi tional 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 minima x decision rule.