Will a Risk-Averse Decision Maker Ever Really Prefer an Unfair Gamble? Sometimes, He Will

摘要

The comments of Horowitz (1998) on the Prakash, Chang, Hamid, and Smyser (1996) paper are specifically directed towards Lemma 4 of the original paper. This reply proposes that Horowitz fails to recognize that the conditions stated are only necessary but not sufficient, and solutions can be obtained for some specific utility function for a given level of wealth in the case of a neutral gamble and for a range of wealth for unfair gambles. We derive the conditions to show that a risk preference function that satisfies the restrictions of Lemma 4 can exist for a given level of wealth.