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Belief heterogeneity in the Arrow-Borch-Raviv insurance model

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  • Ghossoub, Mario

Abstract

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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Bibliographic Info

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

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References

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  1. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2010. "Objective and Subjective Rationality in a Multiple Prior Model," Econometrica, Econometric Society, Econometric Society, vol. 78(2), pages 755-770, 03.
  2. Dirk Bergemann & Stephen Morris, 2010. "Robust Implementation in General Mechanisms," Levine's Working Paper Archive 661465000000000017, David K. Levine.
  3. Robert J. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Working Paper Archive 661465000000000377, David K. Levine.
  4. Dirk Bergemann & Stephen Morris, 2007. "Robust Virtual Implementation," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1609RR, Cowles Foundation for Research in Economics, Yale University, revised Jan 2009.
  5. Massimo Marinacci & Fabio Maccheroni & Alain Chateauneuf & Jean-Marc Tallon, 2003. "Monotone Continuous Multiple Priors," ICER Working Papers - Applied Mathematics Series, ICER - International Centre for Economic Research 30-2003, ICER - International Centre for Economic Research.
  6. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521517324.
  7. Ghossoub, Mario, 2011. "Monotone equimeasurable rearrangements with non-additive probabilities," MPRA Paper 37629, University Library of Munich, Germany, revised 23 Mar 2012.
  8. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, Econometric Society, vol. 57(3), pages 571-87, May.
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  17. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  18. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, Econometric Society, vol. 66(4), pages 929-938, July.
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Citations

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Cited by:
  1. Massimiliano Amarante & Mario Ghossoub & Edmund Phelps, 2012. "Contracting for Innovation under Knightian Uncertainty," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 18-2012, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. 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.
  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, arXiv.org.
  4. Ghossoub, Mario, 2011. "Monotone equimeasurable rearrangements with non-additive probabilities," MPRA Paper 37629, University Library of Munich, Germany, revised 23 Mar 2012.
  5. Amarante, M & Ghossoub, M & Phelps, E, 2013. "Innovation, Entrepreneurship and Knightian Uncertainty," Working Papers, Imperial College, London, Imperial College Business School 12241, Imperial College, London, Imperial College Business School.

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