Skewness preference, risk aversion, and the precedence relations on stochastic changes

This paper provides a general choice-theoretic characterization of the trade-off between risk and skewness, whose importance in understanding risk-taking behavior is well documented in empirical studies. The condition under which the prudence measure characterizes the strength of an individual's downside-risk aversion against his own risk aversion is identified and interpreted in a unifying framework based on the concept of one stochastic dominant change preceding another and that of the desirability of a stochastic change. The framework is also shown to be useful for a better understanding of the Arrow–Pratt measure, the stronger Ross measure, and the coincidence of the characterizations of downside-risk aversion and prudence, as well as the relationship between stochastic dominances of different degrees.