By Robert F. Nau

**Abstract:** A measure of local risk aversion is developed
for choices under uncertainty with non-expected-utility preferences, inseparable
subjective probabilities and state-dependent utilities, and unobserved
stochastic prior wealth. It is assumed only that the decision maker
can assign arbitrage-free marginal prices to risky assets in a manner that
varies smoothly in response to changes in wealth. The risk aversion
measure generalizes the Pratt-Arrow measure and depends only on the risk
neutral probabilities supporting the arbitrage-free prices and on the matrix
of their derivatives with respect to wealth. For decision
makers with non-expected-utility preferences, the measure also incorporates
aversion to uncertainty, i.e., ambiguity or lack of information about probabilities.
As illustrations, the Ellsberg and Allais paradoxes are explained using
a model of “partitionable” smooth preferences that exhibits local uncertainty
aversion at all wealth distributions, unlike Choquet expected utility.
Under this model, the decision maker satisfies the independence axiom selectively
within partitions of the state space whose elements have similar degrees
of uncertainty. As such, she may behave like an expected-utility
maximizer with respect to assets in the same uncertainty class, while exhibiting
higher degrees of risk aversion toward assets that are more uncertain.”