Articles from Cass Knowledge

Double Chain Ladder

This paper presents an extension to the model for forecasting outstanding claims liabilities, formulated by Verrall et al. (2010).

The chain ladder method is one of the most celebrated methods of estimating outstanding liabilities in non-life insurance. Its appeal lies in its simplicity, which is intuitively appealing. It also often gives reasonable results.

The Chain Ladder Method (CLM) operates on aggregate loss data ie - on sums of individual paid (or incurred) claims. From a theoretical point of view this naturally gives rise to a compound Poisson distribution. In this paper a method - related to CLM - is presented that can be formulated as a model of mathematical statistics , and which explicitly acknowledges that data are in fact compound Poisson distributed. While the classical CLM is incapable of dividing predicted outstanding liabilities into RBNS and IBNR claims, we show that our simple regression approach can achieve this in a very concise way. Thus, our approach allows a full model description of the entire cash flow of the outstanding RBNS liabilities. This could prove of huge importance when non-life insurance companies have to meet the requirements of Solvency II.

There are two significant aspects of this model that link it to the CLM. Firstly, it is possible to perform all the estimation necessary for the outstanding claims using just the CLM algorithm. It must be applied twice however, once on incurred count data and then on paid claims data, hence the name "Double Chain Ladder method" (DCL). Secondly, if the fitted (rather than actual) counts are used to produce the forecasts of outstanding claims in the double chain ladder method, the results are exactly the same as those from CLM applied to the triangle of paid claims. Therefore, it is possible to view this model as a different stochastic model to the CLM, as its assumptions are made at the micro claims level.

The full research paper can be downloaded below. Following the introduction, section 2 defines the data used, and sets out the basic first moments assumptions of the model. Section 3 describes the estimation of the first moment parameters. Section 4 describes how to obtain first moment forecasts of outstanding claims and thereby construct the reserves. Section 5 looks at a statistical model with the first moment parameters of DCL. Section 6 contains an illustration of the application of the method to data, and in Section 7 the paper reaches its conclusions.

The authors believe that this method provides a better approach to approximating the CLM than other stochastic models, since it is based on quantities that have a real interpretation in the context of insurance data. Thus, although it is possible to use DCL to reproduce the results of the CLM, we believe that it is better to use it in its purer form, where the assumptions are based on the underlying risk theory.

Along with the research article below we have made available a Double Chain Ladder package that can be viewed following the installation of R software. This software can be downloaded here -

This package provides functions for statistical modelling and forecasting in claims reserving in non-life insurance under the Double Chain Ladder framework. A manual is also available for download below.

This is an alpha version of the software and is still undergoing testing. If you have any comments on it, please direct them to and they will be passed on to the developers.


{Double Chain Ladder}{}; {Presentation - a new R-package for statistical modelling and forecasting in non-life insurance}{}; { DCL R-script - for reproducing illustrations within DCL paper}{}