In this paper, we advance a definition of greater downside risk aversion that applies to both large and small changes in risk preference, and thereby complements the results for small changes reported previously. We show that a downside risk-averse transformation of a utility function results in...

Willingness to take on risk is influenced by the presence of fair and unfair background risks for decision makers who are risk vulnerable as defined by Gollier and Pratt [1996], for these decision makers are more risk averse when they possess such an uninsurable background risk. We present an...

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...