Analagous to the notion of greater risk aversion being that the resulting utility function v = φ(u) is a concave transformation φ of the original utility function u (i.e., φ′′ < 0); the apparent definition of v being more downside risk averse is that φ′ is convex (i.e., φ′′′ > 0). This definition, however, suffers from logical inconsistencies as an ordering. We propose, instead, the...</0);>

An intrinsic, but seldom recognized property of greater risk aversion in expected utility theory is its reversibility, viz., utility v=phi(u) is more risk averse than u if and only if the transformation function phi is concave, while equivalently, u=psi(v) is less risk averse than v if and only...

We present two theorems that yield necessary and sufficient conditions for first and second-degree stochastic dominance deteriorations of background risk to increase risk aversion, prudence, temperance, and all higher degrees of aversion to foreground risk. We thus complete the program initiated...