General Risk Aversion and Attitude Towards Risk

Abstract

THIS PAPER PROPOSES A measure of attitude of individuals towards risk. This measure includes the characteristics of the existing measures as special cases. It enables one to predict how a proportional change in the individual's expected wealth affects his risk premium for a wide range of relationship between the mean wealth and its variance. In their path breaking works, Pratt [3] and Arrow [1] developed two measures U(w) U(w) of risk aversion A(w) =- ( ) and R(w) =- () . w = A(w)w which are U(W) U'w) generally referred to as absolute and relative risk aversion, respectively. U(.) is the von Neumann-Morgenstern utility function defined over an individual's terminal wealth, w, and assumed to be increasing and differentiable. When wealth is a random variable, the measures are defined over expected terminal wealth, ivw, which includes the initial wealth and the expected value of the lottery (Pratt, p. 125). These measures are useful in detecting how variations in the decision-maker's terminal wealth affect his attitude toward a lottery or a risky investment. This is reflected by the induced change in the decision maker's risk premium, 11(w), which was defined by Pratt [3] such that EU(w) = U(w - 11(w)). The risk premium may thus be interpreted as the maximum amount which the decision maker, who is engaged in a lottery, is willing to give up in order to obtain its expected value with certainty. Consequently, the monetary worth which the decision maker assigns to the lottery is measured by its certainty equivalence, w- II(w): It is the minimal amount for which he would be willing to exchange the lottery if he had it. In what follows, the focus will be on these measures of attitude towards risk.