Abstract
The chain ladder method is a popular technique to estimate the future reserves needed to handle claims that are not fully settled. Since the predictions of the aggregate portfolio (consisting of different subportfolios) do not need to be equal to the sum of the predictions of the subportfolios, a general multivariate chain ladder (GMCL) method has already been proposed. However, the GMCL method is based on the seemingly unrelated regression (SUR) technique which makes it very sensitive to outliers. To address this issue, we propose a robust alternative that estimates the SUR parameters in a more outlier resistant way. With the robust methodology it is possible to automatically flag the claims with a significantly large influence on the reserve estimates. We introduce a simulation design to generate artificial multivariate run-off triangles based on the GMCL model and illustrate the importance of taking into account contemporaneous correlations and structural connections between the run-off triangles. By adding contamination to these artificial datasets, the sensitivity of the traditional GMCL method and the good performance of the robust GMCL method is shown. From the analysis of a portfolio from practice it is clear that the robust GMCL method can provide better insight in the structure of the data.
Highlights
Stochastic claims reserving in non-life insurance, known as general insurance in the UK or property and casualty insurance in the US, is an important and challenging discipline for actuaries.Since the claims settlement in non-life insurance may last several years, insurers have to set aside money that enables them to handle the liabilities related to current insurance contracts
We have presented a robust estimation method for the general multivariate chain ladder model proposed by Zhang (2010)
Our proposed methodology takes into account contemporaneous correlations and structural connections between different run-off triangles and still yields reliable results when the data are contaminated
Summary
Stochastic claims reserving in non-life insurance, known as general insurance in the UK or property and casualty insurance in the US, is an important and challenging discipline for actuaries. Zhang (2010) proposed a general multivariate chain ladder (GMCL) model that further extends the MCL model by including intercepts to improve model adequacy The parameters of this flexible model are estimated using the seemingly unrelated regression (SUR) framework. Taking into account the contemporaneous correlations among different portfolios may lead to more accurate uncertainty assessments Another advantage is that structural relationships between triangles where the development of one triangle depends on past losses from other triangles can be included in the GMCL model. The similarity and difference between the GMCL model on bivariate data and the Munich chain ladder model (Quarg and Mack 2004) are discussed by Zhang (2010), who shows that several existing multivariate claims reserving estimators can find their equivalent in the SUR estimator family. The Appendix contains the parameter estimates obtained from the GMCL models for the real dataset
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