Local Utility and Multivariate Risk Aversion
研究了Machina的局部效用如何用于分析多元风险态度，证明了对非期望效用最大化者，多元均值保留风险增加的厌恶等价于局部效用函数的凹性，并扩展了相关结果到多元秩依赖期望效用。
We revisit Machina’s local utility as a tool to analyze attitudes to multivariate risks. We show that for nonexpected 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 [Machina M (1982) “Expected utility” analysis without the independence axiom. Econometrica 50:277–323]. To analyze comparative risk attitudes within the multivariate extension of rank dependent expected utility of Galichon and Henry [Galichon A, Henry M (2012) Dual theory of choice with multivariate risks. J. Econom. Theory 147:1501–1516], we extend Quiggin’s monotone mean and utility preserving increases in risk and show that the useful characterization given in Landsberger and Meilijson [Landsberger M, Meilijson I (1994) Comonotone allocations, Bickel-Lehmann dispersion and the Arrow-Pratt measure of risk aversion. Ann. Oper. Res. 52:97–106] still holds in the multivariate case.