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From Chain-Ladder to Individual Claims Reserving

Ronald Richman, Mario V. Wüthrich

TL;DR

This manuscript introduces a novel approach to computing the CL reserves based on a fundamental restructuring of the data utilization for the CL prediction procedure that estimates multi-period factors that project the latest observations directly to the ultimate claims.

Abstract

The chain-ladder (CL) method is the most widely used claims reserving technique in non-life insurance. This manuscript introduces a novel approach to computing the CL reserves based on a fundamental restructuring of the data utilization for the CL prediction procedure. Instead of rolling forward the cumulative claims with estimated CL factors, we estimate multi-period factors that project the latest observations directly to the ultimate claims. This alternative perspective on CL reserving creates a natural pathway for the application of machine learning techniques to individual claims reserving. As a proof of concept, we present a small-scale real data application employing neural networks for individual claims reserving.

From Chain-Ladder to Individual Claims Reserving

TL;DR

This manuscript introduces a novel approach to computing the CL reserves based on a fundamental restructuring of the data utilization for the CL prediction procedure that estimates multi-period factors that project the latest observations directly to the ultimate claims.

Abstract

The chain-ladder (CL) method is the most widely used claims reserving technique in non-life insurance. This manuscript introduces a novel approach to computing the CL reserves based on a fundamental restructuring of the data utilization for the CL prediction procedure. Instead of rolling forward the cumulative claims with estimated CL factors, we estimate multi-period factors that project the latest observations directly to the ultimate claims. This alternative perspective on CL reserving creates a natural pathway for the application of machine learning techniques to individual claims reserving. As a proof of concept, we present a small-scale real data application employing neural networks for individual claims reserving.
Paper Structure (22 sections, 1 theorem, 34 equations, 3 figures, 9 tables)

This paper contains 22 sections, 1 theorem, 34 equations, 3 figures, 9 tables.

Table of Contents

  1. Addendum
  2. Introduction
  3. Chain-ladder method
  4. Mack's distribution-free chain-ladder model
  5. Recursive chain-ladder factor estimation
  6. Chain-ladder RBNS reserving
  7. Individual ultimate prediction using machine learning
  8. Recursive individual claims reserving
  9. Real data examples
  10. Description of data
  11. Accident insurance data
  12. Liability insurance data
  13. Forecast model
  14. Network architecture
  15. Data pre-processing and model fitting
  16. ...and 7 more sections

Key Result

Proposition 2.2

$\widehat{C}^*_{i,J}=\widehat{C}_{i,J}$ for all accident periods $i\in \{I-J+1, \ldots, I\}$.

Figures (3)

  • Figure 1: Step-wise roll forward (chain-ladder) extrapolation to predict the ultimate claims $C_{i,J}$ using observations $C_{i,I-i}$, $i>I-J$, at time $I$ (for $I=7$ and $J=6$).
  • Figure 2: Backward extrapolation to predict the ultimate claims $C_{i,J}$, $i>I-J$, using the estimated PtU factor estimates $(\widehat{F}_j)_{j=0}^{J-1}$: (left-middle-right) correspond to $j=J-1=5$, $j=4$ and $j=3$.
  • Figure 3: (lhs) Reserves per accident year $i=1,\ldots, 5$ and separated by closed and open claims at time $I$, (rhs) per accident calendar month $cm \in \{1,\ldots, 12\}$.

Theorems & Definitions (1)

  • Proposition 2.2