We present two theorems that provide necessary and sufficient conditions for an expected utility maximizer to become more risk averse in the sense of Ross with respect to bearing a foreground risk after the introduction of any independent fair or unfair additive background risk. We call these...

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...