IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v85y2019icp38-45.html
   My bibliography  Save this article

Equilibrium recoveries in insurance markets with limited liability

Author

Listed:
  • Boonen, Tim J.

Abstract

This paper studies optimal insurance in partial equilibrium in case the insurer is protected by limited liability, and the multivariate insured risk is exchangeable. We focus on the optimal allocation of remaining assets in default. We show existence of an equilibrium in the market. In such an equilibrium, we get perfect pooling of the risk in the market, but a protection fund is needed to charge levies to policyholders with low realized losses. If policyholders cannot be forced ex post to pay a levy, we show that the constrained equal loss rule is used in equilibrium. This rule gained particular interest in the literature on bankruptcy problems. Moreover, in the absence of a regulator, the insurer will always invest all its assets in the risky technology.

Suggested Citation

  • Boonen, Tim J., 2019. "Equilibrium recoveries in insurance markets with limited liability," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 38-45.
    • Handle: RePEc:eee:mateco:v:85:y:2019:i:c:p:38-45
    DOI: 10.1016/j.jmateco.2019.09.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406819301004
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2019.09.001?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. Cummins, J David & Mahul, Olivier, 2003. "Optimal Insurance with Divergent Beliefs about Insurer Total Default Risk," Journal of Risk and Uncertainty, Springer, vol. 27(2), pages 121-138, October.
    2. Rustam Ibragimov & Dwight Jaffee & Johan Walden, 2010. "Pricing and Capital Allocation for Multiline Insurance Firms," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(3), pages 551-578, September.
    3. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357, Elsevier.
    4. Christophe Courbage & Nolwenn Roudaut, 2010. "On Insurance for Long-term Care in France," ifo DICE Report, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, vol. 8(2), pages 24-28, 07.
    5. Helga Habis & P. Herings, 2013. "Stochastic bankruptcy games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 973-988, November.
    6. Emin Karagözoğlu, 2014. "A noncooperative approach to bankruptcy problems with an endogenous estate," Annals of Operations Research, Springer, vol. 217(1), pages 299-318, June.
    7. repec:hal:journl:hal-00538974 is not listed on IDEAS
    8. repec:ces:ifodic:v:8:y:2010:i:2:p:14566966 is not listed on IDEAS
    9. Albrecht, Peter & Huggenberger, Markus, 2017. "The fundamental theorem of mutual insurance," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 180-188.
    10. Su, Karen C., 2010. "The conversion option in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 437-442, June.
    11. John David Cummins & Olivier Mahul, 2003. "Optimal insurance with divergent beliefs about total default risk," Post-Print hal-01952121, HAL.
    12. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    13. Dana, Rose-Anne & Scarsini, Marco, 2007. "Optimal risk sharing with background risk," Journal of Economic Theory, Elsevier, vol. 133(1), pages 152-176, March.
    14. Asimit, Alexandru V. & Badescu, Alexandru M. & Cheung, Ka Chun, 2013. "Optimal reinsurance in the presence of counterparty default risk," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 690-697.
    15. Damir Filipović & Robert Kremslehner & Alexander Muermann, 2015. "Optimal Investment and Premium Policies Under Risk Shifting and Solvency Regulation," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 82(2), pages 261-288, June.
    16. Bruno Jullien & Georges Dionne & Bernard Caillaud, 2000. "Corporate insurance with optimal financial contracting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(1), pages 77-105.
    17. Amy Finkelstein & James Poterba, 2004. "Adverse Selection in Insurance Markets: Policyholder Evidence from the U.K. Annuity Market," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 183-208, February.
    18. Michael Sherris, 2006. "Solvency, Capital Allocation, and Fair Rate of Return in Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(1), pages 71-96, March.
    19. Koster, Maurice & Boonen, Tim J., 2019. "Constrained stochastic cost allocation," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 20-30.
    20. Young, H Peyton, 1990. "Progressive Taxation and Equal Sacrifice," American Economic Review, American Economic Association, vol. 80(1), pages 253-266, March.
    21. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    22. Mohanasundari M. & Dr. Balanaga Gurunathan K, 2010. "Micro Insurance Awareness in Rural India," Journal of Commerce and Trade, Society for Advanced Management Studies, vol. 5(2), pages 74-79, October.
    23. Mário R. Páscoa & Aloisio P. Araujo, 2002. "Bancruptcy in a model of unsecured claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(3), pages 455-481.
    24. John C. Harsanyi, 1953. "Cardinal Utility in Welfare Economics and in the Theory of Risk-taking," Journal of Political Economy, University of Chicago Press, vol. 61(5), pages 434-434.
    25. Neil A. Doherty & Harris Schlesinger, 1990. "Rational Insurance Purchasing: Consideration of Contract Nonperformance," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 105(1), pages 243-253.
    26. Dickson,David C. M., 2010. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521176750.
    27. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63(4), pages 309-309.
    28. Christophe Courbage & Nolwenn Roudaut, 2010. "On Insurance for Long-term Care in France," ifo DICE Report, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, vol. 8(02), pages 24-28, July.
    29. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
    30. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    31. Kıbrıs, Özgür & Kıbrıs, Arzu, 2013. "On the investment implications of bankruptcy laws," Games and Economic Behavior, Elsevier, vol. 80(C), pages 85-99.
    32. Daniel Bauer & George Zanjani, 2016. "The Marginal Cost of Risk, Risk Measures, and Capital Allocation," Management Science, INFORMS, vol. 62(5), pages 1431-1457, May.
    33. Ray Rees & Hugh Gravelle & Achim Wambach, 1999. "Regulation of Insurance Markets," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 24(1), pages 55-68, June.
    34. Laux, Christian & Muermann, Alexander, 2010. "Financing risk transfer under governance problems: Mutual versus stock insurers," Journal of Financial Intermediation, Elsevier, vol. 19(3), pages 333-354, July.
    35. L. C. G. Rogers & L. A. M. Veraart, 2013. "Failure and Rescue in an Interbank Network," Management Science, INFORMS, vol. 59(4), pages 882-898, April.
    36. Denuit, Michel & Vermandele, Catherine, 1998. "Optimal reinsurance and stop-loss order," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 229-233, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Deb Narayan Barik & Siddhartha P. Chakrabarty, 2022. "Does limited liability reduce leveraged risk?: The case of loan portfolio management," Papers 2209.12636, arXiv.org.
    2. Boonen, Tim J. & Liu, Fangda, 2022. "Insurance with heterogeneous preferences," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    3. Reichel, Lukas & Schmeiser, Hato & Schreiber, Florian, 2022. "On the optimal management of counterparty risk in reinsurance contracts," Journal of Economic Behavior & Organization, Elsevier, vol. 201(C), pages 374-394.
    4. Deb Narayan Barik & Siddhartha P. Chakrabarty, 2022. "Does Limited Liability Reduce Leveraged Risk?: The Case of Loan Portfolio Management," JRFM, MDPI, vol. 15(11), pages 1-15, November.
    5. Schumacher, Johannes M., 2021. "Ex-ante estate division under strong Pareto efficiency," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 10-24.
    6. Ben‐jiang Ma & Jing‐yu Ye & Geng Liu & Yuan‐ji Huang, 2020. "Adverse selection, limited compensation, and the design of environmental liability insurance contract in the case of enterprise bankruptcy," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 41(7), pages 1327-1337, October.
    7. Lee, Hangsuck & Ha, Hongjun & Lee, Minha, 2024. "A sharing rule for multi-period interest-sensitive insurance contracts," The North American Journal of Economics and Finance, Elsevier, vol. 71(C).

    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. Koster, Maurice & Boonen, Tim J., 2019. "Constrained stochastic cost allocation," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 20-30.
    2. Long, Yan & Sethuraman, Jay & Xue, Jingyi, 2021. "Equal-quantile rules in resource allocation with uncertain needs," Journal of Economic Theory, Elsevier, vol. 197(C).
    3. Emin Karagözoğlu, 2014. "A noncooperative approach to bankruptcy problems with an endogenous estate," Annals of Operations Research, Springer, vol. 217(1), pages 299-318, June.
    4. Carmen Herrero & Juan Moreno-Ternero & Giovanni Ponti, 2010. "On the adjudication of conflicting claims: an experimental study," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(1), pages 145-179, January.
    5. Andrea Gallice, 2019. "Bankruptcy problems with reference-dependent preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 311-336, March.
    6. Chatterjee, Siddharth & Ertemel, Sinan & Kumar, Rajnish, 2023. "Rationing rules for risky claims," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    7. Markus Huggenberger & Peter Albrecht, 2022. "Risk pooling and solvency regulation: A policyholder's perspective," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(4), pages 907-950, December.
    8. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    9. Schumacher, Johannes M., 2021. "Ex-ante estate division under strong Pareto efficiency," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 10-24.
    10. Juarez, Ruben & Ko, Chiu Yu & Xue, Jingyi, 2018. "Sharing sequential values in a network," Journal of Economic Theory, Elsevier, vol. 177(C), pages 734-779.
    11. Jingyi Xue, 2018. "Fair division with uncertain needs," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(1), pages 105-136, June.
    12. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2012. "A unifying framework for the problem of adjudicating conflicting claims," Journal of Mathematical Economics, Elsevier, vol. 48(2), pages 107-114.
    13. Jaume García-Segarra & Miguel Ginés-Vilar, 2023. "Additive adjudication of conflicting claims," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(1), pages 93-116, March.
    14. Moreno-Ternero, Juan D. & Villar, Antonio, 2004. "The Talmud rule and the securement of agents' awards," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 245-257, March.
    15. Thierry Marchant, 2008. "Scale invariance and similar invariance conditions for bankruptcy problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(4), pages 693-707, December.
    16. Siwei Chen, 2015. "Systematic favorability in claims problems with indivisibilities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(2), pages 283-300, February.
    17. Ketelaars, Martijn & Borm, Peter, 2021. "On the Unification of Centralized and Decentralized Clearing Mechanisms in Financial Networks," Discussion Paper 2021-015, Tilburg University, Center for Economic Research.
    18. Ruben Juarez & Rajnish Kumar, 2013. "Implementing efficient graphs in connection networks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 359-403, October.
    19. Reichel, Lukas & Schmeiser, Hato & Schreiber, Florian, 2022. "On the optimal management of counterparty risk in reinsurance contracts," Journal of Economic Behavior & Organization, Elsevier, vol. 201(C), pages 374-394.
    20. Christopher P. Chambers & Juan D. Moreno-Ternero, 2017. "Taxation and poverty," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 153-175, January.

    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:eee:mateco:v:85:y:2019:i:c:p:38-45. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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.