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Optimal Insurance Under Random Auditing

Author

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  • Marie-Cécile Fagart

    (University of Rouen, THEMA and LEI.)

  • Pierre Picard

    (THEMA (University of Paris X—Nanterre) and CEPREMAP.)

Abstract

We provide a characterization of an optimal insurance contract (coverage schedule and audit policy) when the monitoring procedure is random. When the policyholder exhibits constant absolute risk aversion, the optimal contract involves a positive indemnity payment with a deductible when the magnitude of damages exceeds a threshold. In such a case, marginal damages are fully covered if the claim is verified. Otherwise, there is an additional deductible that disappears when the damages become infinitely large. Under decreasing absolute risk aversion, providing a positive indemnity payment for small claims with a nonmonotonic coverage schedule may be optimal. The Geneva Papers on Risk and Insurance Theory (1999) 24, 29–54. doi:10.1023/A:1008781131861

Suggested Citation

  • Marie-Cécile Fagart & Pierre Picard, 1999. "Optimal Insurance Under Random Auditing," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 24(1), pages 29-54, June.
    • Handle: RePEc:pal:genrir:v:24:y:1999:i:1:p:29-54
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    References listed on IDEAS

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    1. Bond, Eric W. & Crocker, Keith J., 1997. "Hardball and the soft touch: The economics of optimal insurance contracts with costly state verification and endogenous monitoring costs," Journal of Public Economics, Elsevier, vol. 63(2), pages 239-264, January.
    2. Kim C. Border & Joel Sobel, 1987. "Samurai Accountant: A Theory of Auditing and Plunder," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(4), pages 525-540.
    3. Marie-Cécile Fagart & Pierre Picard, 1999. "Optimal Insurance Under Random Auditing," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 24(1), pages 29-54, June.
    4. Dilip Mookherjee & Ivan Png, 1989. "Optimal Auditing, Insurance, and Redistribution," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 104(2), pages 399-415.
    5. David P. Baron & David Besanko, 1984. "Regulation, Asymmetric Information, and Auditing," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 447-470, Winter.
    6. Guesnerie, Roger & Laffont, Jean-Jacques, 1984. "A complete solution to a class of principal-agent problems with an application to the control of a self-managed firm," Journal of Public Economics, Elsevier, vol. 25(3), pages 329-369, December.
    7. Picard, Pierre, 2000. "On the Design of Optimal Insurance Policies under Manipulation of Audit Cost," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1049-1071, November.
    8. GOLLIER, Ch., 1985. "Pareto-optimal risk sharing with fixed costs per claim," LIDAM Discussion Papers CORE 1985046, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Townsend, Robert M., 1979. "Optimal contracts and competitive markets with costly state verification," Journal of Economic Theory, Elsevier, vol. 21(2), pages 265-293, October.
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    Citations

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    Cited by:

    1. Dionne, Georges, 2012. "The empirical measure of information problems with emphasis on insurance fraud and dynamic data," Working Papers 12-10, HEC Montreal, Canada Research Chair in Risk Management.
    2. Thierry Pénard & Saïd Souam, 2002. "Collusion et politique de la concurrence en information asymétrique," Annals of Economics and Statistics, GENES, issue 66, pages 209-233.
    3. Marie-Cécile Fagart & Pierre Picard, 1999. "Optimal Insurance Under Random Auditing," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 24(1), pages 29-54, June.
    4. Daniel J. Clarke, 2011. "Reinsuring the Poor: Group Microinsurance Design and Costly State Verification," Economics Series Working Papers 573, University of Oxford, Department of Economics.
    5. Qin Lian & Harris Schlesinger, 2012. "Insurance Contract Design When the Insurer Has Private Information on Loss Size," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(4), pages 1039-1050, December.
    6. Hau, Arthur, 2008. "Optimal insurance under costly falsification and costly, inexact verification," Journal of Economic Dynamics and Control, Elsevier, vol. 32(5), pages 1680-1700, May.
    7. repec:dau:papers:123456789/6456 is not listed on IDEAS
    8. Jörg Schiller, 2006. "The Impact of Insurance Fraud Detection Systems," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(3), pages 421-438, September.
    9. Kai Sülzle & Achim Wambach, 2005. "Insurance in a Market for Credence Goods," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(1), pages 159-176, March.
    10. Dongsoo Shin & Sungho Yun, 2011. "Granting An Exit Option To Conduct An Audit," Bulletin of Economic Research, Wiley Blackwell, vol. 63(4), pages 438-463, October.
    11. P. Picard, 1998. "Insurance fraud : theory," THEMA Working Papers 98-26, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    12. Bénédicte Coestier & Nathalie Fombaron, 2003. "L'audit en assurance," THEMA Working Papers 2003-41, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    13. Zheng, Jiakun, 2020. "Optimal insurance design under narrow framing," Journal of Economic Behavior & Organization, Elsevier, vol. 180(C), pages 596-607.
    14. Nell, Martin & Schiller, Jörg, 2002. "Erklärungsansätze für vertragswidriges Verhalten von Versicherungsnehmern aus Sicht der ökonomischen Theorie," Working Papers on Risk and Insurance 7, University of Hamburg, Institute for Risk and Insurance.
    15. Richard Watt, 2003. "Curtailing Ex-Post Fraud in Risk Sharing Arrangements," European Journal of Law and Economics, Springer, vol. 16(2), pages 247-263, September.
    16. Guillaume Carlier & Rose-Anne Dana, 2003. "Pareto efficient insurance contracts when the insurer's cost function is discontinuous," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(4), pages 871-893, June.
    17. Pierre Picard, 2012. "Economic Analysis of Insurance Fraud," Working Papers hal-00725561, HAL.
    18. Dionne, Georges & Harrington, Scott, 2017. "Insurance and Insurance Markets," Working Papers 17-2, HEC Montreal, Canada Research Chair in Risk Management.
    19. Katja Müller & Hato Schmeiser & Joël Wagner, 2016. "The impact of auditing strategies on insurers’ profitability," Journal of Risk Finance, Emerald Group Publishing, vol. 17(1), pages 46-79, January.

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    More about this item

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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