Stochastic Dominance Tests for Decreasing Absolute Risk Aversion. I. Discrete Random Variables

Stochastic dominance (SD) theory is concerned with orderings of random variables by classes of utility functions characterized solely in terms of general properties. This paper discusses a type of stochastic dominance, called DSD, which is denned by the utility functions having decreasing absolute risk-aversion. Necessary and sufficient conditions for DSD are presented for discrete random variables which, after the possible addition of points of zero probability, are concentrated on finitely many equally-spaced points. The problem is cast as a nonlinear program, which is solved through an efficient dynamic programming routine. Examples are presented to illustrate the increased effectiveness of DSD relative to previous types of stochastic dominance.