A Robust General Multivariate Chain Ladder Method

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) in general differ from 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 a robust alternative is introduced which estimates the SUR parameters in a more outlier resistant way. With the robust methodology it is possible to detect which claims have an abnormally 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.

Applying State Space Models to Stochastic Claims Reserving

“…The SSMs from Section 3 can be easily generalized for dependent run-off triangles when dealing with correlated lines of business. A single multivariate model exploiting such correlations may improve the IBNR projections generated in the loss reserving processin insurance companies, see, for example, Braun (2004), de Jong (2006, Wüthrich (2007, 2008), Merz et al (2012), Peremans et al (2018), Pröhl and Schmidt (2005), Shi et al (2012), and Zhang (2010). Naturally, in multivariate models, one must estimate the additional parameters describing the correlation among particular triangles which might be in the context of state space methodology (especially, the Kalman recursions) easily performed.…”

“…There are sophisticated methods of robust statistics in the actuarial literature concerning the outliers in run-off triangles (see, e.g., Peremans et al (2018), Pitselis et al (2015), Verdonck and Van Wouwe (2011)). Atherino et al (2010) apply an intervention approach that models the outliers by dummies added to the structural SSM; this approach assumes that one identifies the positions of particular outliers and includes subjective decisions (even though the identified outliers are then verified by statistical tests).…”

Claim Models

“…claim count information. Moving beyond a single homogeneous portfolio, (Avanzi et al (2016) considers the dependencies among lines of business within an insurer's portfolio, while Peremans et al (2018) proposes a robust general multivariate chain ladder approach to accommodate outliers. There is also a category of models, referred to as state space or adaptive models, that allow parameters to evolve recursively in time as more data is observed (Chukhrova and Johannssen 2017).…”

DeepTriangle: A Deep Learning Approach to Loss Reserving

“…Works that propose utilizing data in addition to paid losses include Quarg and Mack [25], which uses incurred losses, and Miranda et al [22], which incorporates claim count information. Moving beyond a single homogeneous portfolio, Avanzi et al [2] considers the dependencies among lines of business within an insurer's portfolio, while Peremans et al [24] proposes a robust general multivariate chain ladder approach to accommodate outliers. There is also a category of models, referred to as state space or adaptive models, that allow parameters to evolve recursively in time as more data is observed [7].…”