Complete monotonicity, background risk, and risk aversion

This paper analyzes how the statistical properties of a risk affect the attitude of individuals towards accepting another independent risk. We conduct the analysis for the class of increasing utility functions having all their derivatives with alternating sign. Such utilities can be expressed as mixtures of negative exponential functions and they are fully described by distribution functions over the set of exponents. Our analysis exploits the relationship between the distribution functions characterizing utilities and the distribution functions characterizing risks. In particular, we find sufficient conditions for an additional background risk to either reduce or increase the index of absolute risk aversion.