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Non-cooperative dynamic games for general insurance markets

Author

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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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    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. 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. Deepanshu Vasal & Randall Berry, 2022. "Master Equation for Discrete-Time Stackelberg Mean Field Games with single leader," Papers 2201.05959, arXiv.org.
    6. Annette Hofmann & Cristina Sattarhoff, 2023. "Underwriting Cycles in Property-Casualty Insurance: The Impact of Catastrophic Events," Risks, MDPI, vol. 11(4), pages 1-25, April.
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    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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