Local utility and multivariate risk aversion

Arthur Charpentier, Alfred Galichon, Marc Henry

    Research output: Contribution to journalArticle

    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 languageEnglish (US)
    Pages (from-to)466-476
    Number of pages11
    JournalMathematics of Operations Research
    Volume41
    Issue number2
    DOIs
    StatePublished - May 2016

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    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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