IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v21y2003i4p871-893.html
   My bibliography  Save this article

Pareto efficient insurance contracts when the insurer's cost function is discontinuous

Author

Listed:
  • Guillaume Carlier
  • Rose-Anne Dana

Abstract

We consider the problem of efficient insurance contracts when the cost structure includes a fixed cost per claim. We prove existence of efficient insurance contracts and that the indemnity function in such contracts is non-decreasing in the damage. We further show that either there is no insurance, or the indemnity is positive for all losses, or efficient insurance contracts have a unique jump. We study variants of the model and provide a generalization to the case of non expected utilities. Our results are then applied to Townsend's model of deterministic auditing. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joecth:v:21:y:2003:i:4:p:871-893
    DOI: 10.1007/s00199-002-0281-z
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00199-002-0281-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00199-002-0281-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. Hong, Chew Soo & Karni, Edi & Safra, Zvi, 1987. "Risk aversion in the theory of expected utility with rank dependent probabilities," Journal of Economic Theory, Elsevier, vol. 42(2), pages 370-381, August.
    4. Chateauneuf, A. & Cohen, M. & Meilijson, I., 1997. "New Tools to Better Model Behavior Under Risk and UNcertainty: An Oevrview," Papiers d'Economie Mathématique et Applications 97.55, Université Panthéon-Sorbonne (Paris 1).
    5. Christian Gollier & Harris Schlesinger, 1996. "Arrow's theorem on the optimality of deductibles: A stochastic dominance approach (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 359-363.
    6. Zilcha, Itzhak & Chew, Soo Hong, 1990. "Invariance of the efficient sets when the expected utility hypothesis is relaxed," Journal of Economic Behavior & Organization, Elsevier, vol. 13(1), pages 125-131, January.
    7. Gur Huberman & David Mayers & Clifford W. Smith Jr., 1983. "Optimal Insurance Policy Indemnity Schedules," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 415-426, Autumn.
    8. 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.
    9. 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).
    10. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
    11. P. Picard, 1998. "Insurance fraud : theory," THEMA Working Papers 98-26, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bénédicte Coestier & Nathalie Fombaron, 2003. "L'audit en assurance," THEMA Working Papers 2003-41, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    2. Cohen Alma, 2006. "The Disadvantages of Aggregate Deductibles," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 6(1), pages 1-28, April.
    3. repec:dau:papers:123456789/5389 is not listed on IDEAS
    4. Carole Bernard & Weidong Tian, 2010. "Insurance Market Effects of Risk Management Metrics," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 35(1), pages 47-80, June.
    5. 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.
    6. Christian Gollier, 2014. "Optimal insurance design of ambiguous risks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 555-576, November.
    7. Dionne, Georges & Harrington, Scott, 2017. "Insurance and Insurance Markets," Working Papers 17-2, HEC Montreal, Canada Research Chair in Risk Management.
    8. Chi, Yichun & Zhou, Xun Yu & Zhuang, Sheng Chao, 2024. "Variance insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 62-82.
    9. Zuo Quan Xu, 2018. "Pareto optimal moral-hazard-free insurance contracts in behavioral finance framework," Papers 1803.02546, arXiv.org, revised Aug 2021.
    10. Pierre Martinon & Pierre Picard & Anasuya Raj, 2018. "On the design of optimal health insurance contracts under ex post moral hazard," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(2), pages 137-185, September.
    11. 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.
    12. J. David Cummins & Olivier Mahul, 2004. "The Demand for Insurance With an Upper Limit on Coverage," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 71(2), pages 253-264, June.
    13. Hangsuck Lee & Minha Lee & Jimin Hong, 2024. "Optimal insurance for repetitive natural disasters under moral hazard," Journal of Economics, Springer, vol. 143(3), pages 247-277, December.
    14. Lu, Zhiyi & Meng, Shengwang & Liu, Leping & Han, Ziqi, 2018. "Optimal insurance design under background risk with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 15-28.
    15. 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.
    16. Michael Breuer, 2005. "Multiple Losses, EX ANTE Moral Hazard, and the Implications for Umbrella Policies," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(4), pages 525-538, December.
    17. Chi, Yichun & Zheng, Jiakun & Zhuang, Shengchao, 2022. "S-shaped narrow framing, skewness and the demand for insurance," Insurance: Mathematics and Economics, Elsevier, vol. 105(C), pages 279-292.
    18. Neil A. Doherty & Christian Laux & Alexander Muermann, 2015. "Insuring Nonverifiable Losses," Review of Finance, European Finance Association, vol. 19(1), pages 283-316.
    19. Carole Bernard & Shaolin Ji & Weidong Tian, 2013. "An optimal insurance design problem under Knightian uncertainty," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 36(2), pages 99-124, November.
    20. Pierre Picard, 2012. "Economic Analysis of Insurance Fraud," Working Papers hal-00725561, HAL.
    21. Chi, Yichun & Zhuang, Sheng Chao, 2022. "Regret-based optimal insurance design," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 22-41.

    More about this item

    Keywords

    Keywords and Phrases: Efficient insurance contracts; Discontinuous cost function; Auditing.; JEL Classification Numbers: C61; G22.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:21:y:2003:i:4:p:871-893. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.