Paper: arXiv 2412.00607

Authors: Hélène Cossette, Benjamin Côté, Alexandre Dubeau, Etienne Marceau

Abstract

In many insurance contexts, dependence between risks of a portfolio may arise from their frequencies. We investigate a dependent risk model in which we assume the vector of count variables to be a tree-structured Markov random field with Poisson marginals. The tree structure translates into a wide variety of dependence schemes. We study the global risk of the portfolio and the risk allocation to all its constituents. We provide asymptotic results for portfolios defined on infinitely growing trees. To illustrate its flexibility and computational scalability to higher dimensions, we calibrate the risk model on real-world extreme rainfall data and perform a risk analysis.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a rigorous theoretical framework extending tree-structured Markov random fields to Poisson marginals with heterogeneous means for risk allocation and aggregate loss calculations. It combines advanced mathematical derivations (asymptotic behavior on infinite trees) with an empirical application to extreme rainfall data, providing both mathematical depth and high computational scalability.

Research Flowchart

  flowchart TD
    A[Research Goal: Model Dependent Risk in Insurance Portfolios via Tree-Structured Frequencies] --> B[Model Formulation: Tree-structured Poisson Markov Random Field]
    C[Data Input: Real-world Extreme Rainfall Data] --> D[Calibration & Computational Analysis]
    B --> D
    D --> E[Theoretical Derivation: Asymptotic Results for Infinitely Growing Trees]
    E --> F[Outcomes: Flexible Portfolio Risk Quantifying & Scalable Risk Allocation]

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2 of 456 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.