RISK AVERSION BEHAVIOR. RELATIONSHIPS BETWEEN RISK AVERSION, PRUDENCE AND CAUTIOUSNESS

This paper defines decreasing absolute risk aversion in purely behavioral termswithout any assumption of differentiability and shows that a strictly increasing and riskaverse utility function with decreasing absolute risk aversion is necessarily differentiable withan absolutely continuous derivative. A risk averse utility function has decreasing absolute riskaversion if and only if it has a decreasing absolute risk aversion density, and if and only if thecumulative absolute risk aversion function is increasing and concave. This leads to acharacterization of all such utility functions. Analogues of these results also hold forincreasing absolute and for increasing and decreasing relative risk aversion.