Paper: arXiv 2507.18207

Authors: Olivier Lopez, Daniel Nkameni

Abstract

In this paper, we address the problem of providing insurance protection against heavy-tailed losses, for which the expected loss may not even be finite. The product we study is based on a combination of traditional insurance up to a given limit and a parametric (or index-based) cover for larger losses. This second component of the coverage is computed from covariates available immediately after the loss occurs, allowing claim management costs to be reduced through rapid compensation. To optimize the design of this second component, we use a criterion adapted to extreme losses, that is, to loss distributions of Pareto type. We support the calibration procedure with theoretical results establishing its convergence rate, as well as empirical evidence from both a simulation study and a real-data analysis on tornado losses in the United States. We also propose a two-step optimization procedure as a potential solution to the issue of data scarcity in the tails of loss distributions. We conclude by empirically demonstrating that the proposed hybrid contract outperforms a traditional capped indemnity contract.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a novel optimization framework designed specifically for heavy-tailed loss distributions by using a loss-to-compensation ratio metric alongside price aversion penalization. The theoretical foundations are supported by mathematical proofs of convergence rates, a synthetic simulation study, and an empirical application to US tornado loss data.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimize hybrid insurance contract <br>for heavy-tailed losses] --> B[Inputs: US Tornado Data & Simulated Pareto Losses]
    B --> C[Methodology: Combine traditional capped cover <br>with parametric index insurance]
    C --> D[Calibration: Optimize extreme-value criterion <br>via EVT & Two-step optimization]
    D --> E[Theoretical Analysis: Establish convergence rates]
    D --> F[Key Outcome: Hybrid contract outperforms <br>traditional capped indemnity]

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0 of 130 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.