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Optimal Underreporting and Competitive Equilibrium

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Listed:
  • Zongxia Liang
  • Jiayu Zhang
  • Zhou Zhou
  • Bin Zou

Abstract

This paper develops a dynamic insurance market model comprising two competing insurance companies and a continuum of insureds, and examines the interaction between strategic underreporting by the insureds and competitive pricing between the insurance companies under a Bonus-Malus System (BMS) framework. For the first time in an oligopolistic setting, we establish the existence and uniqueness of the insureds' optimal reporting barrier, as well as its continuous dependence on the BMS premiums. For the 2-class BMS case, we prove the existence of Nash equilibrium premium strategies and conduct an extensive sensitivity analysis on the impact of the model parameters on the equilibrium premiums.

Suggested Citation

  • Zongxia Liang & Jiayu Zhang & Zhou Zhou & Bin Zou, 2026. "Optimal Underreporting and Competitive Equilibrium," Papers 2601.12655, arXiv.org.
    • Handle: RePEc:arx:papers:2601.12655
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    References listed on IDEAS

    as
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    2. Cao, Jingyi & Li, Dongchen & Young, Virginia R. & Zou, Bin, 2024. "Strategic underreporting and optimal deductible insurance," ASTIN Bulletin, Cambridge University Press, vol. 54(3), pages 767-790, September.
    3. Li, Danping & Young, Virginia R., 2021. "Bowley solution of a mean–variance game in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 35-43.
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    5. Arthur Charpentier & Arthur David & Romuald Elie, 2017. "Optimal Claiming Strategies in Bonus Malus Systems and Implied Markov Chains," Risks, MDPI, vol. 5(4), pages 1-17, November.
    6. S. Zacks & B. Levikson, 2004. "Claiming Strategies and Premium Levels for Bonus Malus Systems," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2004(1), pages 14-27.
    7. Michael Braun & Peter S. Fader & Eric T. Bradlow & Howard Kunreuther, 2006. "Modeling the "Pseudodeductible" in Insurance Claims Decisions," Management Science, INFORMS, vol. 52(8), pages 1258-1272, August.
    8. Cao, Jingyi & Li, Dongchen & Young, Virginia R. & Zou, Bin, 2025. "Continuous-time optimal reporting with full insurance under the mean-variance criterion," Insurance: Mathematics and Economics, Elsevier, vol. 120(C), pages 79-90.
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