Detection and treatment of outliers for multivariate robust loss reserving

TL;DR

This paper introduces two novel robust multivariate techniques for insurance claim reserving that effectively detect and adjust outliers, improving the accuracy of outstanding liability estimates in the presence of skewed and multidimensional data.

Contribution

It extends existing robust reserving methods by incorporating Adjusted Outlyingness and bagdistance, and develops an N-dimensional framework for outlier detection and treatment.

Findings

Effective outlier detection in multivariate reserving data

Improved reserve estimates with robust methods

Application to Australian insurer data demonstrates practicality

Abstract

Traditional techniques for calculating outstanding claim liabilities such as the chain ladder are notoriously at risk of being distorted by outliers in past claims data. Unfortunately, the literature in robust methods of reserving is scant, with notable exceptions such as Verdonck and Debruyne (2011) and Verdonck and Van Wouwe (2011). In this paper, we put forward two alternative robust bivariate chain-ladder techniques to extend the approach of Verdonck and Van Wouwe (2011). The first technique is based on Adjusted Outlyingness (Hubert and Van der Veeken, 2008) and explicitly incorporates skewness into the analysis whilst providing a unique measure of outlyingness for each observation. The second technique is based on bagdistance (Hubert et al., 2016) which is derived from the bagplot however is able to provide a unique measure of outlyingness and a means to adjust outlying observations based on this measure. Furthermore, we extend our robust bivariate chain-ladder approach to an N-dimensional framework. The implementation of the methods, especially beyond bivariate, is not trivial. This is illustrated on a trivariate data set from Australian general insurers, and results under the different outlier detection and treatment mechanisms are compared.