A Stochastic Model Underlying the Chain-Ladder Technique

Renshaw, A. E.; Verrall, Richard

doi:10.1017/s1357321700000222

Cited by 133 publications

(111 citation statements)

References 14 publications

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“…Since Kremer (1982), a variety of statistical models underpinned by the chain-ladder method as well as that allow for an analysis of variability associated with reserve estimates, have been discussed. A generalized linear model was utilized for analyses of the chain-ladder method in Renshaw and Verrall (1998). Mack (1993) introduced a model to calculate the standard error for reserve estimates based on the chain-ladder method when there is an absence of assumptions related to statistical distribution.…”

Section: Literature Reviewmentioning

confidence: 99%

Consideration of a structural-change point in the chain-ladder method

Kwon

2017

CSAM

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The chain-ladder method, for which run-off data is employed is popularly used in the rate-adjustment and loss-reserving practices of non-life-insurance and health-insurance companies. The method is applicable when the underlying assumption of a consistent development pattern is in regards to a cumulative loss payment after the occurrence of an insurance event. In this study, a modified chain-ladder algorithm is proposed for when the assumption is considered to be only partially appropriate for the given run-off data. The concept of a structuralchange point in the run-off data and its reflection in the estimation of unpaid loss amounts are discussed with numerical illustrations. Experience data from private health insurance coverage in Korea were analyzed based on the suggested method. The performance in estimation of loss reserve was also compared with traditional approaches. We present evidence in this paper that shows that a reflection of a structural-change point in the chain-ladder method can improve the risk management of the relevant insurance products. The suggested method is expected to be utilized easily in actuarial practice as the algorithm is straightforward.

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Section: Literature Reviewmentioning

confidence: 99%

Consideration of a structural-change point in the chain-ladder method

Kwon

2017

CSAM

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“…As discussed in Section 1, many distributions such as the lognormal (Kremer, 1982;de Alba, 2002de Alba, , 2006Kunkler, 2004Kunkler, , 2006, over-dispersed Poisson (Renshaw and Verrall, 1998;England et al, 2012), negative binomial (Verrall, 2000) and gamma (de Alba and Nieto-Barajas, 2008) can be assumed for the loss magnitude data. For demonstration purposes, lognormal sampling distributions are assumed for the loss magnitude data y − and y + in our analysis.…”

Section: Modelling Magnitude Datamentioning

confidence: 99%

“…For stochastic reserving (England and Verrall, 2002), specific distributions such as the lognormal (Kremer, 1982), over-dispersed Poisson (Renshaw and Verrall, 1998;England, Verrall and Wuthrich, 2012), negative binomial (Verrall, 2000) and gamma (de Alba and Nieto-Barajas, 2008) are assumed for the loss reserving data. For these models, classical generalized linear model (Nelder and Wedderburn, 1972) structures can be fitted to the mean or other parameters of the reserve distribution.…”

Section: Introductionmentioning

confidence: 99%

A Bayesian Mixture Model Accounting for Zeros and Negatives in the Loss Triangle

Xia

Scollnik²

2015

IJSP

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In insurance loss reserving, a large portion of zeros are expected at the later development periods of an incremental loss triangle. Negative losses occur frequently in the incremental loss triangle due to actuarial practices such as subrogation and salvation. The nature of the distributions assumed by most stochastic models, such as the lognormal and over-dispersed Poisson distributions, brings restrictions on the zeros and negatives appearing in the loss triangle. In this paper, we propose a Bayesian mixture model for stochastic reserving under the situation where there are both zeros and negatives in the incremental loss triangle. A multinomial regression model will be applied to model the sign of the loss data, while the lognormal distribution is assumed for the loss magnitudes of negatives and positives. Bayesian generalized linear models will be fitted for both the mixture and magnitude models. The model will be implemented using the Markov chain Monte Carlo (MCMC) techniques in BUGS. Our model provides a realistic tool for stochastic reserving in the cases of zeros and negatives.

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“…The classical ODP model introduced by Renshaw-Verrall [14] and England-Verrall [5] is one of the most popular stochastic claims reserving models. On the one hand it provides the chain-ladder reserves and on the other hand it is very easy to generate bootstrap samples from.…”

Section: Bayesian Over-dispersed Poisson Modelmentioning

confidence: 99%

Reversible Jump Markov Chain Monte Carlo Method for Parameter Reduction in Claims Reserving

Verrall

Wüthrich

2012

North American Actuarial Journal

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This is the unspecified version of the paper.This version of the publication may differ from the final published version. methods to the important problem of setting claims reserves in general insurance business. PermanentThese reserves are necessary because the premium is received early, but claims may take years to be reported and settled. A measure of the uncertainty in these reserves estimates is also needed for solvency purposes. The RJMCMC methods described in this paper represent an improvement over the manual processes often employed in practice.

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A Stochastic Model Underlying the Chain-Ladder Technique

Cited by 133 publications

References 14 publications

Consideration of a structural-change point in the chain-ladder method

Consideration of a structural-change point in the chain-ladder method

A Bayesian Mixture Model Accounting for Zeros and Negatives in the Loss Triangle

Reversible Jump Markov Chain Monte Carlo Method for Parameter Reduction in Claims Reserving

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