  Stochastic dominance orders are commonly used in both the theory and practice
of risk management and decision making under uncertainty. We provide a novel
characterization of the $n$-th degree bounded stochastic dominance order, which
compares the $n$-th lower partial moments of random variables within a bounded
domain. This characterization establishes a connection between the risk
tolerance of decision-makers and bounded stochastic dominance orders, thereby
providing a decision-theoretic interpretation for these stochastic orders. As a
by-product of our results, we provide applications for portfolio optimization
with stochastic order constraints. We also offer non-trivial inequalities for
$n$-convex functions and rankings over lotteries for decision-makers with a
globally bounded Arrow-Pratt measure of risk aversion. Additionally, we present
comparative statics results regarding savings decisions for decision-makers
with globally bounded prudence measures.
