Stochastic minimax decision rules for risk of extreme events

Author

Wang, Ganghuai ; Lambert, James H. ; Haimes, Yacov Y.

Author_Institution

Virginia Univ., Charlottesville, VA, USA

Volume

29

Issue

6

fYear

1999

fDate

11/1/1999 12:00:00 AM

Firstpage

533

Lastpage

541

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

Keywords

decision theory; minimax techniques; statistical analysis; stochastic processes; CSSD minimax decision rule; FSD; SSD noninferior set size reduction; choice refinement; conditional second-order stochastic dominance; decision rule refinement; decision-maker; extreme event risk; first-order stochastic dominance; order statistics; order statistics SSD minimax decision rule; potential adverse outcomes; probability distribution; random variables; second-order stochastic dominance; stochastic minimax decision rules; Minimax techniques; Probability distribution; Random variables; Risk management; Statistical distributions; Statistics; Stochastic processes; Stochastic systems; Systems engineering and theory; Utility theory;

fLanguage

English

Journal_Title

Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on

Publisher

ieee

ISSN

1083-4427

Type

jour

DOI

10.1109/3468.798057

Filename

798057