Comparative mixed risk aversion: Definition and application to self-protection and willingness to pay

We analyze the optimal choices of agents with utility functions whose derivatives alternate in sign, an important class that includes most of the functions commonly used in economics and finance (Mixed Risk Aversion, MRA, Caballe and Pomansky, 1996). We propose a comparative mixed risk aversion definition for this class of utility functions, namely, "More Risk Averse MRA", and provide a sufficient condition to compare individuals. We apply the model to optimal prevention and willingness to pay. More risk averse MRA agents spend less to reduce accident probabilities that are above 1/2. They spend more only when accident probabilities are below 1/2. Explanations in terms of risk premiums are provided. The results presented also allow for the presence of background risk.