On the impact of outliers in loss reserving

TL;DR

This paper examines how outliers affect loss reserving methods, especially Mack's Model, by deriving impact functions to measure sensitivity and demonstrating the variability of outlier influence across data structures.

Contribution

It introduces impact functions for assessing outlier effects on loss reserves and compares sensitivities between Mack's Model and Bornhuetter-Ferguson methodology.

Findings

Outliers can significantly skew reserve estimates in Mack's Model.

Impact of incremental claims varies widely across the loss triangle.

Impact functions help quantify the sensitivity of reserves to outliers.

Abstract

The sensitivity of loss reserving techniques to outliers in the data or deviations from model assumptions is a well known challenge. It has been shown that the popular chain-ladder reserving approach is at significant risk to such aberrant observations in that reserve estimates can be significantly shifted in the presence of even one outlier. As a consequence the chain-ladder reserving technique is non-robust. In this paper we investigate the sensitivity of reserves and mean squared errors of prediction under Mack's Model (Mack, 1993). This is done through the derivation of impact functions which are calculated by taking the first derivative of the relevant statistic of interest with respect to an observation. We also provide and discuss the impact functions for quantiles when total reserves are assumed to be lognormally distributed. Additionally, comparisons are made between the impact functions for individual accident year reserves under Mack's Model and the Bornhuetter-Ferguson methodology. It is shown that the impact of incremental claims on these statistics of interest varies widely throughout a loss triangle and is heavily dependent on other cells in the triangle. Results are illustrated using data from a Belgian non-life insurer.