Robust loss reserving in a log-linear model
Section snippets
Introduction on loss reserving
The estimation of claim reserves and outstanding claims is very important for the operation of insurance companies, as well as for the determination of the profit. In the actuarial literature there is a variety of papers on loss reserving techniques within the chain ladder framework, namely, Kremer (1982), Taylor and Ashe (1983), Mack, 1991, Mack, 1993, Mack, 1994, Renshaw (1989), Verrall, 1991, Verrall, 2000. The book by Taylor (2000) presents useful material on stochastic methods and
Robust inference
Very often, assumptions, made in statistics, i.e. normality, linearity, independence are at most approximations of reality. Robust regression models are useful for filtering linear relationships when the random variation in the data is not normal or when the data contain significant outliers (see Hampel et al., 1986).
In the following we present a summary of some of the most important robust estimators that appear in the statistical and actuarial literature. Some basic concepts of robust
The log-linear loss reserving models
In this section we revisit two similar models that is the basis for our robust loss reserving estimation: the model of Verrall (1991), who considered the estimation of claims reserves and outstanding claims when a log-linear model is applied and the model of Kremer (1982) who applied the estimation methods of analysis of variance (ANOVA) to the problem of estimating the expected value of IBNR-claims. Typical estimators of the log-normal mean and variance fail to be both efficient and robust. In
Robust log-linear loss reserving model estimation
In this section, we incorporate the robust estimators presented in Section 2 into loss reserving techniques. A robust algorithm for the robustification of the log-linear model of Verrall (1991) is derived as well as a robust estimation in the ANOVA setup of Kremer (1982).
Numerical illustrations
In what it follows we will illustrate the LS and our robust procedures using the data given in Taylor and Ashe (1983) (see Table B.1 in Appendix B). The advantage of using this data set is that is well known and it has been widely used in the actuarial literature (see for example Mack, 1993; England and Verrall, 1999, Verdonck et al., 2009). Our first step is to identify the existence of outlier events (if there are any) in the original data and apply a log-linear regression model, a two way
Overview of the results and concluding remarks
In this work we have shown how robust estimation techniques can be incorporated in a loss reserving framework, providing a fair value for the estimation of outstanding reserves. An overview of the main robust estimators has been given in the first part of the paper. Least squares estimators and robust estimators were applied to Ashe and Taylor data.
Table 6 presents an overview of the robust loss reserving estimation in a log-linear model with the original data (without artificial outliers) and
Acknowledgments
Georgios Pitselis acknowledges the financial support from BOF-SF Senior Fellowships of KU Leuven.
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