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The Arrow–Pratt index of relative risk aversion combines the important economic concepts of elasticity and marginal utility. The index is used by many authors writing in relation to utility theory.
This note explains the classic Arrow-Pratt measure of risk aversion. The standard reference is Pratt (1964) and Arrow (1965). 1 Measures of risk aversion. Consider an agent with expected utility function E[u(w)], where w is wealth and u : R++ ! R is a utility function with u0 > 0 (increasing) and u00 < 0 (concave).
Arrow-Pratt measure of relative risk aversion: Where x is the payoff of a given lottery and U (x) the utility derived from that payoff. In this LP we’ve started by seeing what the difference between risk and uncertainty is.
The Arrow–Pratt measure of relative risk aversion (RRA) or coefficient of relative risk aversion is defined as [11] = = ″ ′ (). Unlike ARA whose units are in $ −1, RRA is a dimensionless quantity, which allows it to be applied universally.
The most common and frequently used measure of risk aversion are the Arrow-Pratt measures of absolute and relative risk-aversion. Named after John W. Pratt’s paper “Risk Aversion in the Small and in the Large”, 1964, and Kenneth Arrow ’s “The Theory of Risk Aversion”, 1965, these are the measures:
measures of risk aversion. The first one is absolute risk aversion: r ((A. x)=−u x )/u ( , which is also called Arrow-Pratt coefficient of absolute risk aversion. Note that u measures the concavity of the utility function, while u normalizes the concavity as the utility representation is unique up to affine transformations. A convenient ...
Key words: marginal utility, risk aversion, scale transformations, stochastic dominances. The Pratt-Arrow absolute risk aversion coef-ficient (Pratt), defined as r(x) = -u''x)/u'x' has been used in many analyses which order alternative action choices under conditions of uncertainty (Cochran, Robison, and Lodwick; Cochran et al.; Danok, McCarl ...
