Paper: arXiv 2405.06235

Authors: Zongxia Liang, Yi Xia, Bin Zou

Abstract

We propose a two-layer stochastic game model to study reinsurance contracting and competition in a market with one insurer and two competing reinsurers. The insurer negotiates with both reinsurers simultaneously for proportional reinsurance contracts that are priced using the variance premium principle. The reinsurance contracting between the insurer and each reinsurer is modeled as a Stackelberg game. The two reinsurers compete for business from the insurer and optimize the so-called relative performance, instead of their own surplus, and their competition is settled by a noncooperative Nash game. We obtain a sufficient and necessary condition, related to the competition degrees of the two reinsurers, for the existence of an equilibrium. We show that the equilibrium, if exists, is unique, and the equilibrium strategy of each player is constant, fully characterized in semiclosed form. Furthermore, we obtain interesting sensitivity results for the equilibrium strategies through both analytical and numerical studies.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a sophisticated theoretical framework combining Stackelberg and Nash stochastic games for reinsurance contracting. While mathematically dense and rigorous with semi-closed form solutions, it lacks real-world empirical validation or backtesting using historical market data.

Research Flowchart

  flowchart TD
    A[Goal: Model Reinsurance Contracting & Competition] --> B[Market Inputs: 1 Insurer, 2 Reinsurers, Variance Premium Principle]
    B --> C[Two-Layer Stochastic Game Framework]
    C --> D[Layer 1: Stackelberg Game<br>Insurer & Reinsurers Negotiation]
    C --> E[Layer 2: Noncooperative Nash Game<br>Reinsurer Competition via Relative Performance]
    D & E --> F[Equilibrium Analysis & Derivation]
    F --> G[Outcomes: Unique Constant Equilibrium,<br>Semiclosed-Form Strategy, Sensitivity Results]

Cited References (35)

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  5. A mean field game approach to optimal investment and risk control for competitive insurers (2024)
  6. Optimal reinsurance with multiple reinsurers: Competitive pricing and coalition stability (2021)
  7. Optimal reinsurance designs based on risk measures: A review (2020)
  8. Stackelberg differential game for insurance under model ambiguity (2022)
and 27 more
  1. Reinsurance games with two reinsurers: Tree versus chain (2023)
  2. Reinsurance games with n variance-premium reinsurers: From tree to chain (2023)
  3. Constrained investment–reinsurance optimization with regime switching under variance premium principle (2016)
  4. On a new paradigm of optimal reinsurance: A stochastic Stackelberg differential game between an insurer and a reinsurer (2018)
  5. Stochastic Stackelberg differential reinsurance games under time-inconsistent mean–variance framework (2019)
  6. Optimal reinsurance under variance related premium principles (2012)
  7. Controlled Markov Processes and Viscosity Solutions (2006)
  8. Optimal robust reinsurance-investment strategies for insurers with mean reversion and mispricing (2018)
  9. On optimal reinsurance treaties in cooperative game under heterogeneous beliefs (2019)
  10. Optimal moral-hazard-free reinsurance under extended distortion premium principles — → 2304.08819
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  13. Stackelberg differential game for reinsurance: Mean-variance framework and random horizon (2022)
  14. Optimal dynamic reinsurance with dependent risks: Variance premium principle (2016)
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  21. Optimal dynamic reinsurance policies under a generalized Denneberg’s absolute deviation principle (2020)
  22. An asymmetric information mean-field type linear-quadratic stochastic Stackelberg differential game with one leader and two followers (2020)
  23. Optimal reinsurance under a new design: two layers and multiple reinsurers (2024)
  24. Stochastic Controls: Hamiltonian Systems and HJB Equations (2012)
  25. Optimal reinsurance under the $\alpha$-maxmin mean-variance criterion (2021)
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2 of 35 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.