Ghossoub, Mario (2010): Belief heterogeneity in the ArrowBorchRaviv insurance model.

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Abstract
In the classical ArrowBorchRaviv problem of demand for insurance contracts, it is wellknown that the optimal insurance contract for an insurance buyer – or decision maker (DM) – is a deductible contract, when the insurer is a riskneutral ExpectedUtility (EU) maximizer, and when the DM is a riskaverse EUmaximizer. In the ArrowBorchRaviv 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.
Item Type:  MPRA Paper 

Original Title:  Belief heterogeneity in the ArrowBorchRaviv insurance model 
Language:  English 
Keywords:  Optimal insurance, deductible contract, subjective probability, heterogeneous beliefs, vigilance, Agreement Theorem, Harsanyi Doctrine, Wilson Doctrine 
Subjects:  D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D86  Economics of Contract: Theory C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C65  Miscellaneous Mathematical Tools G  Financial Economics > G2  Financial Institutions and Services > G22  Insurance ; Insurance Companies ; Actuarial Studies C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods 
Item ID:  37630 
Depositing User:  Mario Ghossoub 
Date Deposited:  28 Mar 2012 16:51 
Last Modified:  23 Feb 2016 13:09 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/37630 