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Non-cooperative dynamic games for general insurance markets

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  • Boonen, Tim J.
  • Pantelous, Athanasios A.
  • Wu, Renchao

Abstract

In the insurance industry, the number of product-specific policies from different companies has increased significantly. The strong market competition has boosted the demand for a competitive premium. In actuarial science, scant literature still exists on how competition actually affects the calculation and the cycles of company’s premiums. In this paper, we model premium dynamics via differential games, and study the insurers’ equilibrium premium dynamics in a competitive market. We apply an optimal control theory methodology to determine the open-loop Nash equilibrium premium strategies. The market power of each insurance company is characterized by a price sensitive parameter, and the business volume is affected by the solvency ratio. We study two models. Considering the average market premiums, the first model studies an exponential relation between premium strategies and volume of business. The second model initially characterizes the competition between any selected pair of insurers, and then aggregates all the paired competitions in the market. Numerical examples illustrate the premium dynamics, and show that premium cycles may exist in equilibrium.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:78:y:2018:i:c:p:123-135
    DOI: 10.1016/j.insmatheco.2017.12.001
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    References listed on IDEAS

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    1. 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.
    2. Emms, Paul, 2007. "Pricing general insurance with constraints," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 335-355, March.
    3. Michael Powers & Martin Shubik & Shun Yao, 1998. "Insurance market games: Scale effects and public policy," Journal of Economics, Springer, vol. 67(2), pages 109-134, June.
    4. Cummins, J. David & Danzon, Patricia M., 1997. "Price, Financial Quality, and Capital Flows in Insurance Markets," Journal of Financial Intermediation, Elsevier, vol. 6(1), pages 3-38, January.
    5. Wu, Renchao & Pantelous, Athanasios A., 2017. "Potential Games With Aggregation In Non-Cooperative General Insurance Markets," ASTIN Bulletin, Cambridge University Press, vol. 47(1), pages 269-302, January.
    6. 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.
    7. Taylor, G. C., 1986. "Underwriting strategy in a competitive insurance environment," Insurance: Mathematics and Economics, Elsevier, vol. 5(1), pages 59-77, January.
    8. Emms, Paul & Haberman, Steven, 2005. "Pricing General Insurance Using Optimal Control Theory," ASTIN Bulletin, Cambridge University Press, vol. 35(2), pages 427-453, November.
    9. Greg Taylor, 2008. "A Simple Model of Insurance Market Dynamics," North American Actuarial Journal, Taylor & Francis Journals, vol. 12(3), pages 242-262.
    10. Martin Jensen, 2010. "Aggregative games and best-reply potentials," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(1), pages 45-66, April.
    11. 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.
    12. Pantelous, Athanasios A. & Passalidou, Eudokia, 2013. "Optimal premium pricing policy in a competitive insurance market environment," Annals of Actuarial Science, Cambridge University Press, vol. 7(2), pages 175-191, September.
    13. Malinovskii, Vsevolod K., 2010. "Competition-Originated Cycles and Insurance Strategies," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 797-843, November.
    14. Paul Emms & Steven Haberman, 2009. "Optimal Management of an Insurer’s Exposure in a Competitive General Insurance Market," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(1), pages 77-105.
    15. Doherty, Neil A. & Kang, Han Bin, 1988. "Interest rates and insurance price cycles," Journal of Banking & Finance, Elsevier, vol. 12(2), pages 199-214, June.
    16. 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.
    17. 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.
    18. Winter Ralph A., 1994. "The Dynamics of Competitive Insurance Markets," Journal of Financial Intermediation, Elsevier, vol. 3(4), pages 379-415, September.
    19. 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.
    20. Lemaire, Jean, 1984. "An Application of Game Theory: Cost Allocation," ASTIN Bulletin, Cambridge University Press, vol. 14(1), pages 61-81, April.
    21. Emms, Paul, 2007. "Dynamic Pricing of General Insurance in a Competitive Market," ASTIN Bulletin, Cambridge University Press, vol. 37(1), pages 1-34, May.
    22. 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.
    23. Paul Emms, 2012. "Equilibrium Pricing of General Insurance Policies," North American Actuarial Journal, Taylor & Francis Journals, vol. 16(3), pages 323-349.
    24. Pantelous, Athanasios A. & Passalidou, Eudokia, 2017. "Optimal strategies for a non-linear premium-reserve model in a competitive insurance market," Annals of Actuarial Science, Cambridge University Press, vol. 11(1), pages 1-19, March.
    25. Lemaire, Jean, 1991. "Cooperative Game Theory and its Insurance Applications," ASTIN Bulletin, Cambridge University Press, vol. 21(1), pages 17-40, April.
    26. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, October.
    27. Aase, Knut K., 1993. "Equilibrium in a Reinsurance Syndicate; Existence, Uniqueness and Characterization," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 185-211, November.
    28. Borch, Karl, 1962. "Application of Game Theory to Some Problems in Automobile Insurance*)," ASTIN Bulletin, Cambridge University Press, vol. 2(2), pages 208-221, September.
    29. A. P. Lerner, 1934. "The Concept of Monopoly and the Measurement of Monopoly Power," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 1(3), pages 157-175.
    30. Taylor, G. C., 1987. "Expenses and underwriting strategy in competition," Insurance: Mathematics and Economics, Elsevier, vol. 6(4), pages 275-287, November.
    31. Tsanakas, Andreas & Christofides, Nicos, 2006. "Risk Exchange with Distorted Probabilities," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 219-243, May.
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    7. Deepanshu Vasal & Randall Berry, 2022. "Master Equation for Discrete-Time Stackelberg Mean Field Games with single leader," Papers 2201.05959, arXiv.org.
    8. 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.

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