Comparative Mixed Risk Aversion : Definition and Application to Self-Protection and Willingness to Pay

Mixed risk aversion (Caballe and Pomansky, 1996) defines the class of increasing utility functions that have derivatives alternating in sign, with positive odd derivatives and negative even derivatives. In this article, we characterize comparative mixed risk aversion so as to answer the following question: how different risk attitudes affect choices when expenditures change event probabilities? Attempts to answer this question in the literature found an endogenous probability. We show that the threshold probability is 1/2 under mixed risk aversion. We consider applications to self-protection and willingness to pay. We obtain that if agent v is more mixed risk averse than agent u, then v will select a higher level of self-protection and will have a higher willingness to pay than u only if the accident probability is lower than 1/2. We extend the results to the presence of a background risk