Paper: arXiv 2512.18790

Authors: Minh Chau Nguyen, Tony S. Wirjanto, Fan Yang

Abstract

Catastrophe risk has long been recognized to pose a serious threat to the insurance sector. Catastrophe risk pooling offers an effective way to diversify losses arising from catastrophic events. In this paper, we investigate a structure of catastrophe risk pool and optimize it so that participants can attain the maximum diversification benefit from joining the pool. Determining the practical optimal pool entails solving a high-dimensional optimization problem, for which analytical solutions are typically unavailable and numerical methods can be computationally intensive and potentially unreliable. To address this challenge, we evaluate the diversification benefit in the limit and use it to derive an asymptotically optimal pool which approximates the practical optimal pool. Through simulation studies, we show that the asymptotically optimal pool provides an accurate and reliable approximation to the practical optimal pool. We also conduct an empirical analysis using data from the U.S. National Flood Insurance Program to illustrate how the framework can be applied in practice.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical contribution by applying asymptotic analysis and extreme value theory to catastrophe risk pooling under heavy-tailed distributions. It balances analytical derivations with simulations and empirical application using NFIP flood loss data.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimize Catastrophe Risk Pool<br/>to Maximize Diversification Benefit] --> B[Input Data: Synthetic Simulations &<br/>U.S. National Flood Insurance Program Data]
    B --> C[Methodology Challenge: Practical Optimization<br/>is High-Dimensional & Computationally Intensive]
    C --> D[Asymptotic Analysis: Evaluate Diversification<br/>Benefit in the Limit to Derive Closed-Form Pool]
    D --> E[Empirical & Numerical Validation: Compare<br/>Asymptotically Optimal Pool to Practical Pool]
    E --> F[Key Outcome: Asymptotic Approach Provides an<br/>Accurate, Reliable, & Efficient Approximation]

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