RISK-AVERSION WITH STATE-DEPENDENT PREFERENCES IN THE RANK-DEPENDENT EXPECTED UTILITY-THEORY

We extend the analysis of risk aversion with state-dependent preferenc es to the rank-dependent expected utility theory. We find that in this extended theory for two preference relations to be comparable in risk aversion not only do their reference sets need to coincide (a conditi on first introduced by Karni [1983, 1985] in the original expected uti lity framework), but they must also rank the prospective state-depende nt outcomes in the same manner. We formalize this additional condition by introducing the concept of certainty sets. Under our condition of comparability, various results and characterizations of interpersonal comparison of risk aversion are obtained. The implications for a speci fic insurance problem are also discussed.