Mack's estimator motivated by large exposure asymptotics in a compound Poisson setting

Paper: arXiv 2310.12056

Authors: Nils Engler, Filip Lindskog

Abstract

The distribution-free chain ladder of Mack justified the use of the chain ladder predictor and enabled Mack to derive an estimator of conditional mean squared error of prediction for the chain ladder predictor. Classical insurance loss models, i.e. of compound Poisson type, are not consistent with Mack’s distribution-free chain ladder. However, for a sequence of compound Poisson loss models indexed by exposure (e.g. number of contracts), we show that the chain ladder predictor and Mack’s estimator of conditional mean squared error of prediction can be derived by considering large exposure asymptotics. Hence, quantifying chain ladder prediction uncertainty can be done with Mack’s estimator without relying on the validity of the model assumptions of the distribution-free chain ladder.

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a strong theoretical contribution by linking Mack’s classic distribution-free chain ladder to compound Poisson models via large exposure asymptotics. However, as a purely mathematical proof-of-concept paper, it lacks empirical backtesting and real-world loss data validation.

Research Flowchart

  flowchart TD
    A["Research Goal: Justify Mack's Estimator via Compound Poisson Models"] --> B["Data/Inputs: Compound Poisson Loss Models indexed by Exposure"]
    B --> C["Methodology: Apply Large Exposure Asymptotics to Loss Data"]
    C --> D["Computational Process: Asymptotic Derivation of Chain Ladder Predictor & MSE"]
    D --> E["Key Finding: Chain Ladder & Mack's Estimator Validated Asymptotically"]
    E --> F["Outcome: Quantify Prediction Uncertainty without Distribution-Free Assumptions"]