Paper: arXiv 2611.06126

Authors: Mario V. Wüthrich

Abstract

We develop a tractable state-space version of the chain-ladder model. The state-space dynamics acts on the accident year axis which, in contrast to the classical chain-ladder model, makes accident years dependent. This state-space version yields an exponential seniority weighting in the chain-ladder factor estimation, and it admits an analytical likelihood representation that enables us to compute the seniority weighted chain-ladder reserves and their prediction uncertainty: the one-year uncertainty is available in closed form and the total uncertainty requires a Monte Carlo simulation from the fully tractable likelihood representation.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a highly mathematical and theoretically sound state-space model for claims reserving, offering a novel approach to exponential seniority weighting. While the empirical section is present, it’s a single numerical example, suggesting room for broader validation. The overall contribution is significant due to its analytical tractability and unified stochastic framework.

Research Flowchart

  flowchart TD
    A[Research Goal: Develop Tractable State-Space Chain-Ladder Model] --> B{Key Methodology: State-Space Dynamics on Accident Year Axis};
    B --> C[Computational Process: Derive Exponential Seniority Weighting];
    C --> D[Data/Inputs: Insurance Loss Triangle (Implicit)];
    D --> E[Computational Process: Analytical Likelihood for Reserves & Uncertainty];
    E --> F[Key Outcome 1: Seniority Weighted Chain-Ladder Reserves];
    E --> G[Key Outcome 2: Prediction Uncertainty (One-year closed form, Total via MC)];