### 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) |
---|---|

Pages (from-to) | 466-476 |

Number of pages | 11 |

Journal | Mathematics of Operations Research |

Volume | 41 |

Issue number | 2 |

DOIs | |

State | Published - May 1 2016 |

### Fingerprint

### 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

### Cite this

*Mathematics of Operations Research*,

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

**Local utility and multivariate risk aversion.** / Charpentier, Arthur; Galichon, Alfred; Henry, Marc.

Research output: Contribution to journal › Article

*Mathematics of Operations Research*, vol. 41, no. 2, pp. 466-476. https://doi.org/10.1287/moor.2015.0736

}

TY - JOUR

T1 - Local utility and multivariate risk aversion

AU - Charpentier, Arthur

AU - Galichon, Alfred

AU - Henry, Marc

PY - 2016/5/1

Y1 - 2016/5/1

N2 - 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.

AB - 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.

KW - Local utility

KW - Multivariate bickel-lehmann dispersion

KW - Multivariate rank dependent utility

KW - Multivariate risk aversion

KW - Pessimism

UR - http://www.scopus.com/inward/record.url?scp=84963763604&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84963763604&partnerID=8YFLogxK

U2 - 10.1287/moor.2015.0736

DO - 10.1287/moor.2015.0736

M3 - Article

AN - SCOPUS:84963763604

VL - 41

SP - 466

EP - 476

JO - Mathematics of Operations Research

JF - Mathematics of Operations Research

SN - 0364-765X

IS - 2

ER -