The Probability Premium and Other Approaches to Higher-degree Comparative Risk Aversion

Abstract: In the framework of expected utility, nth-degree risk aversion/loving is unequivocally characterized by the sign of the nth-order derivative of the utility function, but there exist different notions of one decision maker being nth-degree more risk averse than another. This paper first reformulates Pratt’s (1964) probability premium approach to comparative (2nd-degree) risk aversion with a nonrandom starting wealth, and then shows that the reformulated probability premium approach can be easily extended to deal with random starting wealth and comparative nth-degree risk aversion. The paper shows that interpersonal comparisons of various versions of probability premia for nth-degree risk aversion are characterized by the (n/m)th-degree Ross more risk aversion of Liu and Meyer (2013), where 1n m> ≥. Besides the original Pratt setting, the same comparative nth-degree risk aversion extends to probability premia derived from the risk apportionment setting of Eeckhoudt and Schlesinger (2006) and the comparative statics setting of Jindapon and Neilson (2007)