A Model-Free Continuum of Degrees of Risk Aversion

Abstract

We establish a theory for a continuum of degrees of risk aversion and risk seeking, referred to as fractional risk aversion and risk seeking. The proposed degrees are well defined for any distribution-based monotone preference on any set of prospects; no particular model assumption is required on the preference. The two degrees combined together intuitively reflect a decision-maker's attitude towards risk. We characterize fractional risk aversion and risk seeking in the models of rank-dependent utility (RDU) and cumulative prospect theory (CPT) for four different classes of sets of prospects. For instance, the degree of risk aversion for an RDU preference is equal to the ratio between its index of pessimism and its index of greediness; both indices depend on the set of prospects at consideration.

Keywords: risk aversion, risk seeking, stochastic dominance, expected utility, rank-dependent utility, cumulative prospect theory