A Characterization of the n-th Degree Bounded Stochastic Dominance

Abstract: We provide a novel characterization of the $n$th degree bounded stochastic dominance (BSD) order, linking it to the risk tolerance of decision makers and providing a decision theoretic foundation for these stochastic orders. Our results reveal two contrasting implications, on the positive side, they show that BSD reflects specific risk preferences through the choice of the interval $[a,b]$, by characterizing it in terms of utility functions with globally bounded Arrow Pratt risk aversion or that satisfy an $n$ convexity condition. On the negative side, they highlight limitations of BSD, including the dependence of BSD on the chosen interval and the peculiar risk aversion behavior of decision-makers included in the generator of BSD. We illustrate our results through a portfolio optimization model with stochastic dominance constraints. Additionally, using our characterization, we present comparative statics results for decision making under uncertainty with globally bounded risk aversion measures and savings decisions under globally bounded prudence measures, and derive inequalities for $n$ convex functions.