Mean Square Error of Prediction in the Bornhuetter–Ferguson Claims Reserving Method

This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractThe relationship of the chain ladder method to mathematical statistics has long been debated in actuarial science. During the nineties it became clear that the originally deterministic chain ladder can be seen as an autoregressive time series or as a multiplicative Poisson model. This paper draws on recent research and concludes that chain ladder can be seen as a structured histogram. This gives a direct link between classical aggregate methods and continuous granular methods. When the histogram is replaced by a smooth counter part, we have a continuous chain ladder model. Re-inventing classical chain ladder via double chain ladder and its extensions introduces statistically solid approaches of combining paid and incurred data with direct link to granular data approaches. This paper goes through some of the extensions of double chain ladder and introduces new approaches to incorporating and modelling incurred data.

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“…Some recent papers on the BF method include Verrall (2004), Mack (2008), Schmidt & Zocher (2008), Alai et al . (2009) and Alai et al . (2010).…”

Section: Estimation Of the Parameters In The DCL Modelmentioning

confidence: 95%

The link between classical reserving and granular reserving through double chain ladder and its extensions

Hiabu¹,

Margraf²,

Martínez-Miranda³

et al. 2015

Br. Actuar. J.

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“…The CLM and Bornhuetter-Ferguson (BF) methods are among the easiest claim reserving methods and, due to their simplicity, they are two of the most commonly used techniques in practice. Some recent papers on the BF method include Verrall (2004), Mack (2008), Schmidt and Zocher (2008), Alai et al (2009) and Alai et al (2010). The BF method introduced by Bornhuetter and Ferguson (1972) aims to address one of the well known weaknesses of CLM, which is the effect outliers can have on the estimates of outstanding claims.…”

Section: The Bdcl Methodsmentioning

confidence: 99%

Cash flow generalisations of non-life insurance expert systems estimating outstanding liabilities

Hiabu

Margraf

Martínez-Miranda

et al. 2016

Expert Systems with Applications

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For as long as anyone remembers non-life insurance companies have used the so called chain ladder method to reserve for outstanding liabilities. When historical payments of claims are used as observations then chain ladder can be understood as estimating a multiplicative model. In most non-life insurance companies a mixture of paid data and expert knowledge, incurred data, is used as observations instead of just payments. This paper considers recent statistical cash flow models for asset-liability hedging, capital allocation and other management decision tools, and develops two new such methods incorporating available incurred data expert knowledge into the outstanding liability cash flow model. These two new methods unbundle the incurred data to aggregates of estimates of the future cash flow. By a redistribution to the right algorithm, the estimated future cash flow is incorporated in the overall estimation process and considered as data. A statistical validation technique is developed for these two new methods and they are compared to the other recent cash flow methods. The two methods show to have a very good performance on the real-life data set considered.

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“…This section presents the Bornhuetter-Ferguson interpretation offered by Mack (2000); see also England and Verrall (2002) and Alai et al (2009).…”

Section: Bornhuetter-ferguson Using Levels Of Ultimatesmentioning

confidence: 98%

“…Uniqueness of the estimator. For a full exponential family the likelihood has a maximum if and only if the natural statistic is interior to its convex support, and then the maximum likelihood estimator is unique Barndorff-Nielsen (1978) (Theorem 9.13). The natural statistic T † k = ∑ i,j∈I (Y ij , C 2 , .…”

Section: Proof Of Equationmentioning

confidence: 99%

A Likelihood Approach to Bornhuetter–Ferguson Analysis

Elpidorou

Margraf

Martínez-Miranda

et al. 2019

Risks

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A new Bornhuetter–Ferguson method is suggested herein. This is a variant of the traditional chain ladder method. The actuary can adjust the relative ultimates using externally estimated relative ultimates. These correspond to linear constraints on the Poisson likelihood underpinning the chain ladder method. Adjusted cash flow estimates were obtained as constrained maximum likelihood estimates. The statistical derivation of the new method is provided in the generalised linear model framework. A related approach in the literature, combining unconstrained and constrained maximum likelihood estimates, is presented in the same framework and compared theoretically. A data illustration is described using a motor portfolio from a Greek insurer.

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Mean Square Error of Prediction in the Bornhuetter–Ferguson Claims Reserving Method

Cited by 24 publications

References 18 publications

The link between classical reserving and granular reserving through double chain ladder and its extensions

The link between classical reserving and granular reserving through double chain ladder and its extensions

Cash flow generalisations of non-life insurance expert systems estimating outstanding liabilities

A Likelihood Approach to Bornhuetter–Ferguson Analysis

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