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
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 - http://cran.r-project.org/
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 firstname.lastname@example.org
and they will be passed on to the developers.