RISK SEEKING WITH DIMINISHING MARGINAL UTILITY IN A NONEXPECTED UTILITY MODEL

The present work takes place in the framework of a non-expected utility model under risk: the RDEU theory (Rank Dependent Expected Utility, first initiated by Quiggin under the denomination of Anticipated Utility), where the decision maker's behavior is characterized by two functions u and f. Our first result gives a condition under which the function u characterizes the decision maker's attitude towards wealth. Then, defining a decision maker as risk averter (respectively risk seeker) when he always prefers to any random variable its expected value (weak definition of risk aversion), the second result states that a decision maker who has an increasing marginal utility of wealth (a convex function u) can be risk averse, if his function f is ''sufficiently below'' his function u, hence if he is sufficiently ''pessimistic.'' Obviously, he can also be risk seeking with a diminishing marginal utility of wealth. This result is noteworthy because with a stronger definition of risk aversion/risk seeking, based on mean-preserving spreads, Chew, Kami, and Safra have shown that the only way to be risk averse (in their sense) in RDEU theory is to have, simultaneously, a concave function u and a convex function.