Local Utility and Multivariate Risk Aversion

TL;DR

This paper extends the concept of local utility to multivariate risks, providing new characterizations of risk aversion and attitudes in complex decision-making models beyond expected utility.

Contribution

It generalizes Machina's local utility framework to multivariate risks and extends risk attitude characterizations within multivariate rank-dependent utility models.

Findings

Multivariate risk aversion corresponds to local utility concavity.

Extended Quiggin's risk increase concepts to multivariate rank-dependent utility.

Characterization of risk attitudes remains valid in multivariate settings.

Abstract

We revisit Machina's local utility as a tool to analyze attitudes to multivariate risks. We show that for non-expected utility maximizers choosing between multivariate prospects, aversion to multivariate mean preserving increases in risk is equivalent to the concavity of the local utility functions, thereby generalizing Machina's result in Machina (1982). To analyze comparative risk attitudes within the multivariate extension of rank dependent expected utility of Galichon and Henry (2011), we extend Quiggin's monotone mean and utility preserving increases in risk and show that the useful characterization given in Landsberger and Meilijson (1994) still holds in the multivariate case.