IDEAS home Printed from https://ideas.repec.org/a/bla/mathfi/v32y2022i2p595-626.html
   My bibliography  Save this article

Fairness principles for insurance contracts in the presence of default risk

Author

Listed:
  • Delia Coculescu
  • Freddy Delbaen

Abstract

We use the theory of cooperative games for the design of fair insurance contracts. An insurance contract needs to specify the premium to be paid and a possible participation in the benefit (or surplus) of the company. We suppose that a convex commonotonic premium functional is used to value the aggregated liability of the insurance company. It results from the analysis that when a contract is exposed to the default risk of the insurance company, ex‐ante equilibrium considerations require a certain participation in the benefit of the company to be specified in the contracts. The fair benefit participation of agents appears as an outcome of a game involving the residual risks induced by the default possibility and using fuzzy coalitions.

Suggested Citation

  • Delia Coculescu & Freddy Delbaen, 2022. "Fairness principles for insurance contracts in the presence of default risk," Mathematical Finance, Wiley Blackwell, vol. 32(2), pages 595-626, April.
    • Handle: RePEc:bla:mathfi:v:32:y:2022:i:2:p:595-626
    DOI: 10.1111/mafi.12344
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/mafi.12344
    Download Restriction: no
    File URL: https://libkey.io/10.1111/mafi.12344?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
    ---><---

    References listed on IDEAS

    as
    1. Deprez, Olivier & Gerber, Hans U., 1985. "On convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 4(3), pages 179-189, July.
    2. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    3. DELBAEN, Freddy, 1974. "Convex games and extreme points," LIDAM Reprints CORE 159, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Louis J. Billera & David C. Heath, 1982. "Allocation of Shared Costs: A Set of Axioms Yielding A Unique Procedure," Mathematics of Operations Research, INFORMS, vol. 7(1), pages 32-39, February.
    5. Damir Filipović & Michael Kupper, 2008. "Equilibrium Prices For Monetary Utility Functions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(03), pages 325-343.
    6. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    7. repec:dau:papers:123456789/361 is not listed on IDEAS
    8. E. Jouini & W. Schachermayer & N. Touzi, 2008. "Optimal Risk Sharing For Law Invariant Monetary Utility Functions," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 269-292, April.
    9. David Heath & Hyejin Ku, 2004. "Pareto Equilibria with coherent measures of risk," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 163-172, April.
    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. Acciaio, Beatrice & Svindland, Gregor, 2009. "Optimal risk sharing with different reference probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 426-433, June.
    2. Rose-Anne Dana & Cuong Le Van, 2009. "No-arbitrage, overlapping sets of priors and the existence of efficient allocations and equilibria in the presence of risk and ambiguity," Post-Print halshs-00281582, HAL.
    3. Li, Peng & Lim, Andrew E.B. & Shanthikumar, J. George, 2010. "Optimal risk transfer for agents with germs," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 1-12, August.
    4. Tsanakas, Andreas, 2009. "To split or not to split: Capital allocation with convex risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 268-277, April.
    5. Grechuk, Bogdan, 2023. "Extended gradient of convex function and capital allocation," European Journal of Operational Research, Elsevier, vol. 305(1), pages 429-437.
    6. Rose-Anne Dana & Cuong Le Van, 2008. "No-arbitrage, overlapping sets of priors and the existence of efficient allocations and equilibria in the presence of risk and ambiguity," Documents de travail du Centre d'Economie de la Sorbonne b08039, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Nov 2009.
    7. Mitja Stadje, 2018. "Representation Results for Law Invariant Recursive Dynamic Deviation Measures and Risk Sharing," Papers 1811.09615, arXiv.org, revised Dec 2018.
    8. Knispel, Thomas & Laeven, Roger J.A. & Svindland, Gregor, 2016. "Robust optimal risk sharing and risk premia in expanding pools," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 182-195.
    9. Stadje, M.A. & Pelsser, A., 2014. "Time-Consistent and Market-Consistent Evaluations (Revised version of 2012-086)," Discussion Paper 2014-002, Tilburg University, Center for Economic Research.
    10. Rose-Anne Dana & Cuong Le Van, 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," Post-Print halshs-00470670, HAL.
    11. Antoon Pelsser & Mitja Stadje, 2014. "Time-Consistent And Market-Consistent Evaluations," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 25-65, January.
    12. Boonen, Tim J., 2017. "Risk Redistribution Games With Dual Utilities," ASTIN Bulletin, Cambridge University Press, vol. 47(1), pages 303-329, January.
    13. Gao, Feng & Song, Fengming & Zhang, Lihong, 2007. "Coherent risk measure, equilibrium and equilibrium pricing," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 85-94, January.
    14. Grechuk, Bogdan, 2015. "The center of a convex set and capital allocation," European Journal of Operational Research, Elsevier, vol. 243(2), pages 628-636.
    15. Rose-Anne Dana & Cuong Le Van, 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," PSE-Ecole d'économie de Paris (Postprint) halshs-00470670, HAL.
    16. Tim J. Boonen & Fangda Liu & Ruodu Wang, 2021. "Competitive equilibria in a comonotone market," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1217-1255, November.
    17. Burgert, Christian & Rüschendorf, Ludger, 2008. "Allocation of risks and equilibrium in markets with finitely many traders," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 177-188, February.
    18. Michail Anthropelos & Gordan Žitković, 2010. "Partial equilibria with convex capital requirements: existence, uniqueness and stability," Annals of Finance, Springer, vol. 6(1), pages 107-135, January.
    19. Nicole EL KAROUI & Claudia RAVANELLI, 2008. "Cash Sub-additive Risk Measures and Interest Rate Ambiguity," Swiss Finance Institute Research Paper Series 08-09, Swiss Finance Institute.
    20. Marcelo Brutti Righi & Marlon Ruoso Moresco, 2024. "Inf-convolution and optimal risk sharing with countable sets of risk measures," Annals of Operations Research, Springer, vol. 336(1), pages 829-860, May.

    More about this item

    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:bla:mathfi:v:32:y:2022:i:2:p:595-626. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627 .

    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.