Risk Aversion in Cumulative Prospect Theory

This paper characterizes the conditions for risk aversion in cumulative prospect theory where risk aversion is defined in the strong sense of Rothschild and Stiglitz (1970). Under weaker assumptions than differentiability we show that risk aversion implies convex weighting functions for gains and for losses but not necessarily a concave utility function. Also, we investigate the exact relationship between loss aversion and risk aversion. We illustrate the analysis by considering two special cases of cumulative prospect theory and show that risk aversion and convex utility may coexist.