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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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  17. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
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  22. Ghossoub, Mario, 2011. "Monotone equimeasurable rearrangements with non-additive probabilities," MPRA Paper 37629, University Library of Munich, Germany, revised 23 Mar 2012.
  23. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, July.
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