Possibilistic Risk Aversion

Abstract

Risk aversion is a main theme of risk theory. Its objective is to describe the subjective attitude of an agent towards a risk situation. Theory of risk aversion became an autonomous research direction by results of Arrow [2], [3] and Pratt [64],who introduced a way to measure the attitude of an agent towards risk by defining a coeficient of risk aversion in terms of the utility functions. Important contributions in theory of risk aversion were due to Ross [67], Pratt and Zeckhauser [65], Diamond and Stieglitz [20], Kimball [51], Quiggin [66], etc. Traditionally, risk aversion is studied by probabilistic methods. The probabilistic framework in wich risk aversion is treated consists of two components: a random variable which models the experience in which risk appears and a utility function which represents the attitude of the agent with respect to various outcomes of this experience. The main concepts of risk aversion theory are defined in terms of probabilistic indicators (expected value, variance, covariance, etc. ). This chapter concerns a possibilistic approach to risk aversion. We shall develop this theory in a framework defined by a fuzzy number and a utility function. The fuzzy number will describe the risk situation and the utility function will express the attitude of the agent. We will present two approaches to possibilistic risk aversion, corresponding to two notions of expected utility.