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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.

Suggested Citation

  • Ghossoub, Mario, 2010. "Belief heterogeneity in the Arrow-Borch-Raviv insurance model," MPRA Paper 37630, University Library of Munich, Germany, revised 22 Mar 2012.
  • Handle: RePEc:pra:mprapa:37630

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    References listed on IDEAS

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    Cited by:

    1. Massimiliano Amarante & Mario Ghossoub & Edmund Phelps, 2012. "Contracting for Innovation under Knightian Uncertainty," Cahiers de recherche 18-2012, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. Amarante, M & Ghossoub, M & Phelps, E, 2013. "Innovation, Entrepreneurship and Knightian Uncertainty," Working Papers 12241, Imperial College, London, Imperial College Business School.
    3. Rodrigo S. Targino & Gareth W. Peters & Georgy Sofronov & Pavel V. Shevchenko, 2013. "Optimal insurance purchase strategies via optimal multiple stopping times," Papers 1312.0424,
    4. Ghossoub, Mario, 2011. "Monotone equimeasurable rearrangements with non-additive probabilities," MPRA Paper 37629, University Library of Munich, Germany, revised 23 Mar 2012.
    5. Ghossoub, Mario, 2010. "Supplement to "Belief heterogeneity in the Arrow-Borch-Raviv insurance model"," MPRA Paper 37717, University Library of Munich, Germany, revised 22 Mar 2012.

    More about this item


    Optimal insurance; deductible contract; subjective probability; heterogeneous beliefs; vigilance; Agreement Theorem; Harsanyi Doctrine; Wilson Doctrine;

    JEL classification:

    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics


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