A Characterization of Bounded Stochastic Dominance

Bar Light, Andres Perlroth

Published 2022-12-14Version 1

Stochastic dominance orders are commonly used in the theory and practice of risk management and decision making under uncertainty. We provide a novel characterization for the $n$-th degree bounded stochastic dominance order which compares the $n$-th lower partial moment of the random variables under consideration on a bounded domain. This characterization establishes a connection between the risk tolerance of decision makers and bounded stochastic dominance orders, and hence, it provides a decision theoretic interpretation for these stochastic orders. As a by-product of our results, we provide non-trivial inequalities for $n$-convex functions and rankings over lotteries for decision makers with a globally bounded Arrow-Pratt measure of risk aversion.