### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 466-476 |

Number of pages | 11 |

Journal | Mathematics of Operations Research |

Volume | 41 |

Issue number | 2 |

DOIs | |

State | Published - May 2016 |

### Keywords

- Local utility
- Multivariate bickel-lehmann dispersion
- Multivariate rank dependent utility
- Multivariate risk aversion
- Pessimism

### ASJC Scopus subject areas

- Mathematics(all)
- Computer Science Applications
- Management Science and Operations Research

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## Cite this

*Mathematics of Operations Research*,

*41*(2), 466-476. https://doi.org/10.1287/moor.2015.0736