Tradeoffs for Downside Risk-Averse Decision-Makers and the Self-Protection Decision

Abstract

Besides risk aversion, decision makers are often assumed to be downside risk averse. In order to investigate tradeoffs that downside risk averse decision makers face, this paper proposes five stochastic orders, each corresponding to a tradeoff involving a downside risk increase. In addition to obtaining their respective CDF characterizations, these orders are also combined with Ross more risk aversion and two versions of Ross more downside risk aversion to produce comparative static theorems identifying the choices of decision makers relative to that of a reference decision maker. The paper concludes with analysis of the decision to self-protect, a decision that increases downside risk along with making other changes. This exercise not only shows that all five stochastic orders studied in this paper find corresponding tradeoffs in the self-protection model, it also demonstrates that these five tradeoffs are the only meaningful tradeoffs that the standard self-protection model creates. Therefore, the concepts and results presented here provide a systematic and complete treatment of the relationship between self-protection and risk preferences.