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Belief heterogeneity in the Arrow-Borch-Raviv insurance model

  • Ghossoub, Mario

In the classical Arrow-Borch-Raviv problem of demand for insurance contracts, it is well-known that the optimal insurance contract for an insurance buyer – or decision maker (DM) – is a deductible contract, when the insurer is a risk-neutral Expected-Utility (EU) maximizer, and when the DM is a risk-averse EU-maximizer. In the Arrow-Borch-Raviv framework, however, both parties share the same probabilistic beliefs about the realizations of the underlying insurable loss. This paper argues for heterogeneity of beliefs in the classical insurance model, and considers a setting where the DM and the insurer have preferences yielding different subjective beliefs. The DM seeks the insurance contract that will maximize her (subjective) expected utility of terminal wealth with respect to her subjective probability measure, whereas the insurer sets premiums on the basis of his subjective probability measure. I show that in this setting, and under a consistency requirement on the insurer’s subjective probability that I call vigilance, there exists an event to which the DM assigns full (subjective) probability and on which an optimal insurance contract for the DM takes the form of what I will call a generalized deductible contract. Moreover, the class of all optimal contracts for the DM that are nondecreasing in the loss is fully characterized in terms of their distribution under the DM’s probability measure. Finally, the assumption of vigilance is shown to be a weakening of the assumption of a monotone likelihood ratio, when the latter can be defined, and it is hence a useful tool in situations where the likelihood ratio cannot be defined.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 37630.

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Date of creation: 10 Jun 2010
Date of revision: 22 Mar 2012
Handle: RePEc:pra:mprapa:37630
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  1. Dirk Bergemann & Stephen Morris, 2005. "Ex Post Implementation," Cowles Foundation Discussion Papers 1502, Cowles Foundation for Research in Economics, Yale University.
  2. Lehrer, Ehud & Samet, Dov, 2011. "Agreeing to agree," Theoretical Economics, Econometric Society, vol. 6(2), May.
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  4. Meglena Jeleva & Bertrand Villeneuve, 1997. "Insurance Contracts with Imprecise Probabilities and Adverse Selection," Working Papers 97-16, Centre de Recherche en Economie et Statistique.
  5. Ghossoub, Mario, 2011. "Monotone equimeasurable rearrangements with non-additive probabilities," MPRA Paper 37629, University Library of Munich, Germany, revised 23 Mar 2012.
  6. Dirk Bergemann & Stephen Morris, 2008. "Robust Implementation in General Mechanisms," Cowles Foundation Discussion Papers 1666R, Cowles Foundation for Research in Economics, Yale University, revised Jan 2010.
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  10. Dirk Bergemann & Stephen Morris, 2009. "Robust Virtual Implementation," Levine's Working Paper Archive 814577000000000155, David K. Levine.
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  12. Alain Chateauneuf & Fabio Macheronni & Massimo Marinacci & Jean-Marc Tallon, 2005. "Monotone continuous multiple priors," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00177057, HAL.
  13. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2010. "Objective and Subjective Rationality in a Multiple Prior Model," Econometrica, Econometric Society, vol. 78(2), pages 755-770, 03.
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  16. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  17. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, July.
  18. Shavell, Steven, 1979. "On Moral Hazard and Insurance," The Quarterly Journal of Economics, MIT Press, vol. 93(4), pages 541-62, November.
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