Risk-Aversion Concepts in Expected- and Non-Expected-Utility Models

The non-expected-utility theories of decision under risk have favored the appearance of new notions of increasing risk like monotone increasing risk (based on the notion of comonotonic random variables) or new notions of risk aversion like aversion to monotone increasing risk, in better agreement with these new theories. After a survey of all the possible notions of increasing risk and of risk aversion and their intrinsic definitions, we show that contrary to expected-utility theory where all the notions of risk aversion have the same characterization ( u concave), in the framework of rank-dependent expected utility (one of the most well known of the non-expectedutility models), the characterizations of all these notions of risk aversion are different. Moreover, we show that, even in the expected-utility framework, the new notion of monotone increasing risk can give better answers to some problems of comparative statics such as in portfolio choice or in partial insurance. This new notion also can suggest more intuitive approaches to inequalities measurement. The Geneva Papers on Risk and Insurance Theory (1995) 20, 73–91. doi:10.1007/BF01098959