Stochastic Dominance Tests for Decreasing Absolute Risk-Aversion II: General Random Variables

Abstract

Necessary and sufficient conditions are given for stochastic dominance over the class of decreasing absolute risk-averse utility functions. The random variables being compared may be continuous as well as discrete but are assumed to be bounded from below, to have finite means, to have only finitely many mass points in finite intervals, and to have cumulative distribution functions which cross one another only finitely many times, or touch one another only finitely many times in finite intervals. The precise forms of the dominance tests depend upon the number of times the distribution functions cross. An example of the DSD test is presented, and a dynamic programming algorithm for carrying out the general test is given.

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