Local Utility and Multivariate Risk Aversion

We revisit Machina's local utility as a tool to analyze attitudes to multivariate risks. Using martingale embedding techniques, 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. To analyze comparative risk attitudes within the multivariate extension of rank dependent expected utility, we extend Quiggin's monotone mean and utility preserving increases in risk and show that the useful characterization given still holds in the multivariate case