Paper: arXiv 2611.08968

Authors: Colin Priest

Abstract

A claims-development movement on one portfolio may not transfer directly as a stress to another size. We estimate how to transfer such scenarios between portfolio sizes, using 632 syndicate-years from 117 Lloyd’s syndicates over 2015-2024. The measured movement is the change in gross claims estimates on selected older underwriting cohorts, divided by opening gross claims outstanding plus reserves taken on in the year whose development it includes; it is not a pure measure of opening-reserve deterioration. Its dispersion falls materially with reserve size, and a size-based scale predicts held-out syndicates far better than a single market scale. But the transferred upper tail understates the smallest books: in the smallest reserve-size quartile, six of 158 held-out observations exceeded the transferred 99.5th percentile, against 0.79 expected, from three syndicates. Square-root scaling has descriptively lower held-out pinball loss at 99% and 99.5%, though more misses among the largest books. For a GBP 500m portfolio the transferred empirical 99.5th percentile is 0.34 of reserves (95% credible interval, conditional on the fitted model, 0.23-0.52), against 0.67 in the raw market pool. Both are Syndicate 5820’s 2016 movement. The contribution is inspectable scenario comparability, not a calibrated capital quantile or a next-year forecast.

Complexity vs Empirical Score

  • Math Complexity: 6.0/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs a clear quantitative methodology to analyze real-world insurance data, demonstrating strong empirical rigor. While the mathematical complexity is moderate, the application to scenario transfer in reserve movements is novel and well-executed. The paper is well-structured and provides sufficient detail for understanding the approach.

Research Flowchart

  flowchart TD
    A[Research Goal: Transfer Claims Development Scenarios Between Portfolio Sizes] --> B{Methodology: Quantify Reserve Movement Dispersion & Transferability};
    B --> C[Data: 632 Syndicate-Years from 117 Lloyd's Syndicates (2015-2024)];
    C --> D{Computational Process: Estimate Gross Claims Movement & Size-Based Scaling};
    D --> E[Finding 1: Dispersion Falls with Reserve Size; Size-Based Scale Outperforms Market Scale];
    E --> F[Finding 2: Transferred Upper Tail Understates Smallest Books (e.g., Smallest Quartile: 6 of 158 exceeded 99.5th percentile vs 0.79 expected)];
    F --> G[Finding 3: Square-root Scaling has Lower Held-out Pinball Loss at 99%/99.5%];
    G --> H[Outcome: Inspectable Scenario Comparability, Not Calibrated Capital Quantile/Forecast];