Ein neuer Ansatz zur Frequenzmodellierung im Versicherungswesen (A new Approach to frequency modeling in risk theory)

Paper: arXiv 2309.04483

Authors: Dietmar Pfeifer

Abstract

The collective risk model differentiates usually between claims frequencies (and their distribution) and claim sizes (and their distribution). For the claims frequencies typically classical discrete distributions are considered, such as Binomial-, Negative binomial- or Poisson distributions. Since these distributions sometimes do not really fit to the data we propose a different approach here for claim frequencies via random proportions of the number of insurance contracts. This approach also allows for a statistical goodness-of-fit test via quantile-quantile-plots and can likewise be applied to the modelling of claim size distributions.

Complexity vs Empirical Score

• Math Complexity: 5.5/10
• Empirical Rigor: 4.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces a novel approach to claim frequency modeling using random proportions rather than standard discrete distributions, supported by parametric probability theory. However, the empirical evaluation relies heavily on conceptual Q-Q plot testing rather than extensive real-world backtesting or large dataset validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Improve Claim Frequency Modeling in Collective Risk Model] --> B[Inputs: Insurance Contracts & Historical Claim Data]
    B --> C[New Methodology: Model Claim Frequencies via Random Proportions of Contracts]
    C --> D[Model Extension: Apply Random Proportions Approach to Claim Size Distributions]
    D --> E[Statistical Validation: Perform Goodness-of-Fit Tests using Q-Q Plots]
    E --> F[Key Outcome: Better Fitting Model & Visual Diagnostic Tool over Classical Poisson/Binomial Models]