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Pricing in a competitive stochastic insurance market

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  • Mourdoukoutas, Fotios
  • Boonen, Tim J.
  • Koo, Bonsoo
  • Pantelous, Athanasios A.

Abstract

This paper studies a one-period stochastic game to determine the optimal premium strategies of non-life insurers in a competitive market. Specifically, the optimal premium strategy is determined by the Nash equilibrium of an n-player game, in which each player is assumed to maximise the expected utility of terminal wealth. The terminal wealth is stochastic, since the number of policies and the size of claims are considered to be random variables. The total loss of each insurer is described by the collective risk model. The expected number of policies is affected by all the premiums in the market and further investigated by two distinct demand functions. Both models have an exponential functional form, that is characterised by market and price sensitivity parameters. The demand in the first model is zero for premiums above a given threshold, whereas the second model does not include such restriction. The pure strategy Nash equilibrium premiums are given as solutions to constrained optimisation problems. For the first model we prove the existence and uniqueness of a pure strategy Nash equilibrium, whereas for the second model we provide a formula when it exists. Two numerical examples are provided to illustrate the applicability of our findings.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:insuma:v:97:y:2021:i:c:p:44-56
    DOI: 10.1016/j.insmatheco.2021.01.003
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    1. 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.
    2. Rob Kaas & Marc Goovaerts & Jan Dhaene & Michel Denuit, 2008. "Modern Actuarial Risk Theory," Springer Books, Springer, edition 2, number 978-3-540-70998-5, June.
    3. 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.
    4. Terry L. Friesz, 2010. "Dynamic Optimization and Differential Games," International Series in Operations Research and Management Science, Springer, number 978-0-387-72778-3, April.
    5. 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.
    6. Lemaire, Jean, 1984. "An Application of Game Theory: Cost Allocation," ASTIN Bulletin, Cambridge University Press, vol. 14(1), pages 61-81, April.
    7. Emms, Paul, 2007. "Dynamic Pricing of General Insurance in a Competitive Market," ASTIN Bulletin, Cambridge University Press, vol. 37(1), pages 1-34, May.
    8. Taylor, G. C., 1986. "Underwriting strategy in a competitive insurance environment," Insurance: Mathematics and Economics, Elsevier, vol. 5(1), pages 59-77, January.
    9. Paul Emms, 2012. "Equilibrium Pricing of General Insurance Policies," North American Actuarial Journal, Taylor & Francis Journals, vol. 16(3), pages 323-349.
    10. Emms, Paul & Haberman, Steven, 2005. "Pricing General Insurance Using Optimal Control Theory," ASTIN Bulletin, Cambridge University Press, vol. 35(2), pages 427-453, November.
    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. Lemaire, Jean, 1991. "Cooperative Game Theory and its Insurance Applications," ASTIN Bulletin, Cambridge University Press, vol. 21(1), pages 17-40, April.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Taylor, G. C., 1987. "Expenses and underwriting strategy in competition," Insurance: Mathematics and Economics, Elsevier, vol. 6(4), pages 275-287, November.
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    More about this item

    Keywords

    Competitive markets; Non-cooperative game theory; Nash equilibrium; Convex and concave demand functions; Stochastic claims;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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