Paper: arXiv 2601.12655

Authors: 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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework extending Bonus-Malus underreporting models into an oligopolistic competitive equilibrium context using dynamic programming and Stackelberg games. However, it is primarily microeconomic/actuarial theory with theoretical proofs and sensitivity analyses rather than empirical validation on real-world datasets.

Research Flowchart

  flowchart TD
    A[Research Goal: Model Strategic Underreporting & Competitive Pricing in Oligopolistic Insurance Market] --> B[Model Inputs: 2 Competing Insurers, Continuum of Insureds, 2-Class BMS]
    B --> C[Methodology: Dynamic Game Theory & Bonus-Malus System Framework]
    C --> D[Computational Process 1: Determine Insureds' Optimal Reporting Barrier]
    C --> E[Computational Process 2: Prove & Calculate Nash Equilibrium Premium Strategies]
    D --> F[Key Outcomes: Unique Optimal Barrier Found & Nash Equilibrium Proven with Sensitivity Analysis]
    E --> F

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and 34 more
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0 of 42 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.