Risk and Uncertainty Aversion with Reference to the Theories Of Expected Utility, Rank Dependent Expected Utility, and Choquet Expected Utility.

Abstract

The notion of risk aversion originates from Bernoulli’s proposal of introducing the certainty equivalent of a lottery through its expected utility. This proposal implies, if the utility function is concave, a positive risk premium, where the risk premium of a lottery is the difference between its expected value and its certainty equivalent. Pratt (1964) based his notion of risk aversion on the risk premium and he introduced a measure of risk aversion (the well known Arrow-Pratt measure of risk aversion), which strictly depends on the concavity of the utility function. This result occurs since Pratt (as well as {ptde} Finetti, 1952, and Arrow, 1965) adopted the expected utility theory. However, we can also use the risk premium when a non-expected utility theory is adopted. With regard to these theories, which represent the preference preordering on the set of lotteries by means of a utility function which is non-linear in the probabilities of consequences, we find that the risk premium depends on the non-linearity in the probabilities much more than on the non-linearity in the consequences (i.e., on the concavity of the utility function of the consequences). This result leads to the distinction between the risk aversion of the first order and the risk aversion of the second order (Montesano, 1988 and 1991, Hilton, 1988, and Segal and Spivak, 1990).