Risk aversion and prudence in the large

The familiar measures of absolute and relative risk aversion constructed by Pratt and Arrow, along with the measures of absolute and relative prudence inspired by Leland and later developed by Kimball, are local instruments based on the first and second derivatives of utility at a specific level of wealth. As such, they are applicable only to infinitesimal risks—those for which differential calculus is a suitable analytical tool. Consequently, they may not accurately gauge preferences regarding the larger risks typically encountered in practice. To address this problem, the present paper develops more general, closed-form index measures of risk aversion and prudence that are applicable to either large or small risks. The new measures are exact in that they do not rely on approximations, they can be implemented empirically without knowledge of the functional form of utility, and they do not require information regarding pre-existing wealth.