Paper: arXiv 2412.01704

Authors: Ziyue Shi, David Landriault, Fangda Liu

Abstract

In the literature, insurance and reinsurance pricing is typically determined by a premium principle, characterized by a risk measure that reflects the policy seller’s risk attitude. Building on the work of Meyers (1980) and Chen et al. (2016), we propose a new performance-based variable premium scheme for reinsurance policies, where the premium depends on both the distribution of the ceded loss and the actual realized loss. Under this scheme, the insurer and the reinsurer face a random premium at the beginning of the policy period. Based on the realized loss, the premium is adjusted into either a ‘‘reward’’ or ‘‘penalty’’ scenario, resulting in a discount or surcharge at the end of the policy period. We characterize the optimal reinsurance policy from the insurer’s perspective under this new variable premium scheme. In addition, we formulate a Bowley optimization problem between the insurer and the monopoly reinsurer. Numerical examples demonstrate that, compared to the expected-value premium principle, the reinsurer prefers the variable premium scheme as it reduces the reinsurer’s total risk exposure.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical formulation using distortion risk measures, optimal control/indemnity functions, and Bowley optimization for reinsurance design. However, it relies entirely on synthetic/numerical examples rather than real-world empirical loss datasets, placing it firmly in the theoretical ‘Lab Rats’ domain.

Research Flowchart

  flowchart TD
    A[Research Goal: Develop & Optimize Performance-Based Variable Premium Reinsurance Scheme] --> B[Inputs: Ceded Loss Distribution, Realized Loss & Risk Measures]
    B --> C[Formulate Variable Premium Scheme: Base Premium + Adjustment]
    C --> D[Derive Optimal Reinsurance Policy for Insurer]
    D --> E[Model Bowley Optimization Game: Insurer vs. Monopoly Reinsurer]
    E --> F[Conduct Numerical Experiments & Comparative Analysis]
    F --> G[Key Outcome: Variable Scheme Reduces Reinsurer Risk Exposure vs. Expected-Value Principle]

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