IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v231y2013i3p702-711.html
   My bibliography  Save this article

Competition among non-life insurers under solvency constraints: A game-theoretic approach

Author

Listed:
  • Dutang, Christophe
  • Albrecher, Hansjoerg
  • Loisel, Stéphane

Abstract

We formulate a noncooperative game to model competition for policyholders among non-life insurance companies, taking into account market premium, solvency level, market share and underwriting results. We study Nash equilibria and Stackelberg equilibria for the premium levels, and give numerical illustrations.

Suggested Citation

  • Dutang, Christophe & Albrecher, Hansjoerg & Loisel, Stéphane, 2013. "Competition among non-life insurers under solvency constraints: A game-theoretic approach," European Journal of Operational Research, Elsevier, vol. 231(3), pages 702-711.
    • Handle: RePEc:eee:ejores:v:231:y:2013:i:3:p:702-711
    DOI: 10.1016/j.ejor.2013.06.029
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221713005365
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2013.06.029?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. K A Smith & R J Willis & M Brooks, 2000. "An analysis of customer retention and insurance claim patterns using data mining: a case study," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(5), pages 532-541, May.
    2. Chiappori, Pierre-Andre & Durand, Franck & Geoffard, Pierre-Yves, 1998. "Moral hazard and the demand for physician services: First lessons from a French natural experiment," European Economic Review, Elsevier, vol. 42(3-5), pages 499-511, May.
    3. Mattias K. Polborn, 1998. "A Model of an Oligopoly in an Insurance Market," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 23(1), pages 41-48, June.
    4. Borch, Karl, 1975. "Optimal Insurance Arrangements," ASTIN Bulletin, Cambridge University Press, vol. 8(3), pages 284-290, September.
    5. Anna Heusinger & Christian Kanzow, 2009. "Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions," Computational Optimization and Applications, Springer, vol. 43(3), pages 353-377, July.
    6. Loisel, Stéphane & Milhaud, Xavier, 2011. "From deterministic to stochastic surrender risk models: Impact of correlation crises on economic capital," European Journal of Operational Research, Elsevier, vol. 214(2), pages 348-357, October.
    7. Diewert, W. E. & Avriel, M. & Zang, I., 1981. "Nine kinds of quasiconcavity and concavity," Journal of Economic Theory, Elsevier, vol. 25(3), pages 397-420, December.
    8. Julien Hardelin & Sabine Lemoyne de Forges, 2012. "Raising Capital in an Insurance Oligopoly Market," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 37(1), pages 83-108, March.
    9. A. Y. Golubin, 2006. "Pareto‐Optimal Insurance Policies in the Models with a Premium Based on the Actuarial Value," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(3), pages 469-487, September.
    10. Takagoshi, Noritsugu & Matsubayashi, Nobuo, 2013. "Customization competition between branded firms: Continuous extension of product line from core product," European Journal of Operational Research, Elsevier, vol. 225(2), pages 337-352.
    11. Taylor, G. C., 1986. "Underwriting strategy in a competitive insurance environment," Insurance: Mathematics and Economics, Elsevier, vol. 5(1), pages 59-77, January.
    12. Pierre Picard, 2014. "Participating Insurance Contracts and the Rothschild-Stiglitz Equilibrium Puzzle," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 39(2), pages 153-175, September.
    13. Kliger, Doron & Levikson, Benny, 1998. "Pricing insurance contracts -- an economic viewpoint," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 243-249, July.
    14. Stéphane Loisel, 2011. "Surrender risk and correlation crises," Post-Print hal-00671919, HAL.
    15. Simon P. Anderson & André De Palma & Jacques-François Thisse, 1989. "Demand for Differentiated Products, Discrete Choice Models, and the Characteristics Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(1), pages 21-35.
    16. Emms, P. & Haberman, S. & Savoulli, I., 2007. "Optimal strategies for pricing general insurance," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 15-34, January.
    17. Taksar, Michael & Zeng, Xudong, 2011. "Optimal non-proportional reinsurance control and stochastic differential games," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 64-71, January.
    18. Chen, Yun Chu & Fang, Shu-Cherng & Wen, Ue-Pyng, 2013. "Pricing policies for substitutable products in a supply chain with Internet and traditional channels," European Journal of Operational Research, Elsevier, vol. 224(3), pages 542-551.
    19. Michael Rothschild & Joseph Stiglitz, 1976. "Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(4), pages 629-649.
    20. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    21. Dimitriyadis, Irini & TektaS, Arzu, 1998. "A note on the behavior of the insureds in auto-insurance systems in Turkey," European Journal of Operational Research, Elsevier, vol. 106(1), pages 39-44, April.
    22. Lemaire, Jean & Quairiere, Jean-Pierre, 1986. "Chains of Reinsurance Revisited," ASTIN Bulletin, Cambridge University Press, vol. 16(2), pages 77-88, November.
    23. Powers, Michael R. & Shubik, Martin, 1998. "On the tradeoff between the law of large numbers and oligopoly in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 23(2), pages 141-156, November.
    24. Borch, Karl, 1960. "Reciprocal Reinsurance Treaties," ASTIN Bulletin, Cambridge University Press, vol. 1(4), pages 170-191, December.
    25. 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.
    26. Onn, Keet Peng & Mercer, Alan, 1998. "The direct marketing of insurance," European Journal of Operational Research, Elsevier, vol. 109(3), pages 541-549, September.
    27. Mary A. Weiss, 2007. "Underwriting Cycles: A Synthesis and Further Directions," Journal of Insurance Issues, Western Risk and Insurance Association, vol. 30(1), pages 31-46.
    28. Taylor, G. C., 1987. "Expenses and underwriting strategy in competition," Insurance: Mathematics and Economics, Elsevier, vol. 6(4), pages 275-287, November.
    29. Leung, Chi Man & Kwok, Yue Kuen, 2012. "Patent-investment games under asymmetric information," European Journal of Operational Research, Elsevier, vol. 223(2), pages 441-451.
    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. Asimit, Alexandru V. & Boonen, Tim J. & Chi, Yichun & Chong, Wing Fung, 2021. "Risk sharing with multiple indemnity environments," European Journal of Operational Research, Elsevier, vol. 295(2), pages 587-603.
    2. Malinovskii, Vsevolod K., 2015. "Business planning for a profit-seeking insurer under deficiency of information," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 215-226.
    3. Asmussen, Søren & Christensen, Bent Jesper & Thøgersen, Julie, 2019. "Nash equilibrium premium strategies for push–pull competition in a frictional non-life insurance market," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 92-100.
    4. Mourdoukoutas, Fotios & Boonen, Tim J. & Koo, Bonsoo & Pantelous, Athanasios A., 2021. "Pricing in a competitive stochastic insurance market," Insurance: Mathematics and Economics, Elsevier, vol. 97(C), pages 44-56.
    5. Chen, Lv & Shen, Yang & Su, Jianxi, 2020. "A continuous-time theory of reinsurance chains," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 129-146.
    6. Boonen, Tim J. & Pantelous, Athanasios A. & Wu, Renchao, 2018. "Non-cooperative dynamic games for general insurance markets," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 123-135.
    7. Runze Yang & Ruigang Zhang, 2022. "Environmental Pollution Liability Insurance and Corporate Performance: Evidence from China in the Perspective of Green Development," IJERPH, MDPI, vol. 19(19), pages 1-18, September.
    8. Dalit Daily-Amir & Hansjörg Albrecher & Martin Bladt & Joël Wagner, 2019. "On Market Share Drivers in the Swiss Mandatory Health Insurance Sector," Risks, MDPI, vol. 7(4), pages 1-25, November.
    9. Mendonça, Francisco V. & Catalão-Lopes, Margarida & Marinho, Rui Tato & Figueira, José Rui, 2020. "Improving medical decision-making with a management science game theory approach to liver transplantation," Omega, Elsevier, vol. 94(C).
    10. Alavi Fard, Farzad & Sy, Malick & Ivanov, Dmitry, 2019. "Optimal overbooking strategies in the airlines using dynamic programming approach in continuous time," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 128(C), pages 384-399.
    11. Cao, Jingyi & Li, Dongchen & Young, Virginia R. & Zou, Bin, 2023. "Reinsurance games with two reinsurers: Tree versus chain," European Journal of Operational Research, Elsevier, vol. 310(2), pages 928-941.
    12. Boonen, Tim J., 2016. "Nash equilibria of Over-The-Counter bargaining for insurance risk redistributions: The role of a regulator," European Journal of Operational Research, Elsevier, vol. 250(3), pages 955-965.
    13. Barsotti, Flavia & Milhaud, Xavier & Salhi, Yahia, 2016. "Lapse risk in life insurance: Correlation and contagion effects among policyholders’ behaviors," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 317-331.
    14. José Daniel López-Barrientos & Ekaterina Viktorovna Gromova & Ekaterina Sergeevna Miroshnichenko, 2020. "Resource Exploitation in a Stochastic Horizon under Two Parametric Interpretations," Mathematics, MDPI, vol. 8(7), pages 1-29, July.
    15. Claire Mouminoux & Christophe Dutang & Stéphane Loisel & Hansjoerg Albrecher, 2022. "On a Markovian Game Model for Competitive Insurance Pricing," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1061-1091, June.
    16. Florin Avram & Romain Biard & Christophe Dutang & Stéphane Loisel & Landy Rabehasaina, 2014. "A survey of some recent results on Risk Theory," Post-Print hal-01616178, HAL.
    17. Dimitrova, Dimitrina S. & Kaishev, Vladimir K. & Zhao, Shouqi, 2015. "On finite-time ruin probabilities in a generalized dual risk model with dependence," European Journal of Operational Research, Elsevier, vol. 242(1), pages 134-148.
    18. Cheung, Ka Chun & Yam, Sheung Chi Phillip & Zhang, Yiying, 2019. "Risk-adjusted Bowley reinsurance under distorted probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 64-72.
    19. Søren Asmussen & Bent Jesper Christensen & Julie Thøgersen, 2019. "Stackelberg Equilibrium Premium Strategies for Push-Pull Competition in a Non-Life Insurance Market with Product Differentiation," Risks, MDPI, vol. 7(2), pages 1-23, May.

    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. repec:hal:wpaper:hal-00746245 is not listed on IDEAS
    2. Asmussen, Søren & Christensen, Bent Jesper & Thøgersen, Julie, 2019. "Nash equilibrium premium strategies for push–pull competition in a frictional non-life insurance market," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 92-100.
    3. Claire Mouminoux & Christophe Dutang & Stéphane Loisel & Hansjoerg Albrecher, 2022. "On a Markovian Game Model for Competitive Insurance Pricing," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1061-1091, June.
    4. Boonen, Tim J. & Pantelous, Athanasios A. & Wu, Renchao, 2018. "Non-cooperative dynamic games for general insurance markets," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 123-135.
    5. Søren Asmussen & Bent Jesper Christensen & Julie Thøgersen, 2019. "Stackelberg Equilibrium Premium Strategies for Push-Pull Competition in a Non-Life Insurance Market with Product Differentiation," Risks, MDPI, vol. 7(2), pages 1-23, May.
    6. Marko Backovic & Zoran Popovic & Mladen Stamenkovic, 2016. "Reflexive Game Theory Approach to Mutual Insurance Problem," Montenegrin Journal of Economics, Economic Laboratory for Transition Research (ELIT), vol. 12(3), pages 87-100.
    7. José Daniel López-Barrientos & Ekaterina Viktorovna Gromova & Ekaterina Sergeevna Miroshnichenko, 2020. "Resource Exploitation in a Stochastic Horizon under Two Parametric Interpretations," Mathematics, MDPI, vol. 8(7), pages 1-29, July.
    8. Christensen, Bent Jesper & Parra-Alvarez, Juan Carlos & Serrano, Rafael, 2021. "Optimal control of investment, premium and deductible for a non-life insurance company," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 384-405.
    9. Julien Hardelin & Sabine Lemoyne de Forges, 2012. "Raising Capital in an Insurance Oligopoly Market," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 37(1), pages 83-108, March.
    10. Dionne, Georges & Harrington, Scott, 2017. "Insurance and Insurance Markets," Working Papers 17-2, HEC Montreal, Canada Research Chair in Risk Management.
    11. Georges Dionne & Nathalie Fombaron & Neil Doherty, 2012. "Adverse Selection in Insurance Contracting," Cahiers de recherche 1231, CIRPEE.
    12. Mourdoukoutas, Fotios & Boonen, Tim J. & Koo, Bonsoo & Pantelous, Athanasios A., 2021. "Pricing in a competitive stochastic insurance market," Insurance: Mathematics and Economics, Elsevier, vol. 97(C), pages 44-56.
    13. Jir^o Akahori & Yuuki Ida & Maho Nishida & Shuji Tamada, 2020. "The Thermodynamic Approach to Whole-Life Insurance: A Method for Evaluation of Surrender Risk," Papers 2012.09606, arXiv.org.
    14. Radoslav Raykov, 2014. "Uncertain Costs and Vertical Differentiation in an Insurance Duopoly," Staff Working Papers 14-14, Bank of Canada.
    15. Pantelous, Athanasios A. & Passalidou, Eudokia, 2015. "Optimal premium pricing strategies for competitive general insurance markets," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 858-874.
    16. Barsotti, Flavia & Milhaud, Xavier & Salhi, Yahia, 2016. "Lapse risk in life insurance: Correlation and contagion effects among policyholders’ behaviors," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 317-331.
    17. Hyojoung Kim & Doyoung Kim & Subin Im & James W. Hardin, 2009. "Evidence of Asymmetric Information in the Automobile Insurance Market: Dichotomous Versus Multinomial Measurement of Insurance Coverage," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(2), pages 343-366, June.
    18. Renaud Bourlès & Dominique Henriet, 2012. "Risk-sharing Contracts with Asymmetric Information," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 37(1), pages 27-56, March.
    19. Renaud Bourlès, 2006. "How Can Insurance Companies Compete With MutualInsurers? The Role of Commitment," Working Papers halshs-00410765, HAL.
    20. Benjamin Lester & Ali Shourideh & Venky Venkateswaran & Ariel Zetlin-Jones, 2019. "Screening and Adverse Selection in Frictional Markets," Journal of Political Economy, University of Chicago Press, vol. 127(1), pages 338-377.
    21. Borglin, Anders & Flåm, Sjur Didrik, 2007. "Risk exchange as a market or production game," Working Papers in Economics 09/07, University of Bergen, Department of Economics.

    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:ejores:v:231:y:2013:i:3:p:702-711. 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/eor .

    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.