Greater downside risk aversion in the large

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 riskaverse transformation of a utility function results in a function that is more downside risk averse in the same manner that a risk-averse transformation increases risk aversion. Our demonstration is conducted first by using the compensated approach introduced by Diamond and Stiglitz (1974) and then by using an adaptation of the risk premium approach taken by Pratt (1964).