Co-monotone allocations, Bickel-Lehmann dispersion and the Arrow-Pratt measure of risk aversion

Michael Landsberger*, Isaac Meilijson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

For every integrable allocation (X1, X2, ..., Xn) of a random endowment Y=Σi=1/nXi among n agents, there is another allocation (X1*, X2*, ..., Xn*) such that for every 1≤i≤n, Xi* is a nondecreasing function of Y (or, (X1*, X2*, ..., Xn*) are co-monotone) and Xi* dominates Xi by Second Degree Dominance. If (X1*, X2*, ..., Xn*) is a co-monotone allocation of Y=Σi=1/nXi*, then for every 1≤i≤n, Y is more dispersed than Xi* in the sense of the Bickel and Lehmann stochastic order. To illustrate the potential use of this concept in economics, consider insurance markets. It follows that unless the uninsured position is Bickel and Lehmann more dispersed than the insured position, the existing contract can be improved so as to raise the expected utility of both parties, regardless of their (concave) utility functions.

Original languageEnglish
Pages (from-to)97-106
Number of pages10
JournalAnnals of Operations Research
Volume52
Issue number2
DOIs
StatePublished - Jun 1994

Keywords

  • Bickel-Lehmann dispersion
  • Co-monotonicity

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