Risk Aversion and Insurance Propensity

We provide a new foundation of risk aversion by showing that this attitude is fully captured by the propensity to seize insurance opportunities. Our foundation, which applies to all probabilistically sophisticated preferences, well accords with the commonly held prudential interpretation of risk aversion that dates back to the seminal works of Arrow (1963) and Pratt (1964). In our main results, we first characterize the Arrow-Pratt risk aversion in terms of propensity to full insurance and the stronger notion of risk aversion of Rothschild and Stiglitz (1970) in terms of propensity to partial insurance. We then extend the analysis to comparative risk aversion by showing that the notion of Yaari (1969) corresponds to comparative propensity to full insurance, while the stronger notion of Ross (1981) corresponds to comparative propensity to partial insurance.