Analytic and bootstrap estimates of prediction errors in claims reserving

England, Peter D.; Verrall, Richard

doi:10.1016/s0167-6687(99)00016-5

Cited by 124 publications

(141 citation statements)

References 11 publications

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“…As an over-dispersed Poisson example, we chose the data set by Taylor and Ashe (1983) in Table 1 which has become a sort of benchmark data set for this model. Verrall (1991), England and Verrall (1999), and Pinheiro et al (2003) all use this data, to name but a few. Finally, the data by Barnett and Zehnwirth (2000) seem to require a calendar effect for modeling; we take this opportunity to demonstrate that we can easily test for specification in a model with an extended chain-ladder structure that includes a calendar effect.…”

Section: Empirical Applicationsmentioning

confidence: 99%

“…Unlike the Poisson model, the over-dispersed Poisson model is moment-based and does not come equipped with a distributional framework. Despite this shortcoming, distribution forecasts are needed and bootstrapping England and Verrall 1999) is in widespread use. Yet, so far we do not have a statistical theory for the bootstrap in this setting.…”

Section: Introductionmentioning

confidence: 99%

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Misspecification Tests for Log-Normal and Over-Dispersed Poisson Chain-Ladder Models

Harnau

2018

Risks

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Despite the widespread use of chain-ladder models, so far no theory was available to test for model specification. The popular over-dispersed Poisson model assumes that the over-dispersion is common across the data. A further assumption is that accident year effects do not vary across development years and vice versa. The log-normal chain-ladder model makes similar assumptions. We show that these assumptions can easily be tested and that similar tests can be used in both models. The tests can be implemented in a spreadsheet. We illustrate the implementation in several empirical applications. While the results for the log-normal model are valid in finite samples, those for the over-dispersed Poisson model are derived for large cell mean asymptotics which hold the number of cells fixed. We show in a simulation study that the finite sample performance is close to the asymptotic performance.

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Section: Empirical Applicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Misspecification Tests for Log-Normal and Over-Dispersed Poisson Chain-Ladder Models

Harnau

2018

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“…Note that the definition of θ * shares many features with, e.g., Buchwalder et al (2006), as well as England and Verrall (1999).…”

Section: Bias and Msepmentioning

confidence: 99%

Valuation of Non-Life Liabilities from Claims Triangles

Lindholm

Lindskog

Wahl

2017

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This paper provides a complete program for the valuation of aggregate non-life insurance liability cash flows based on claims triangle data. The valuation is fully consistent with the principle of valuation by considering the costs associated with a transfer of the liability to a so-called reference undertaking subject to capital requirements throughout the runoff of the liability cash flow. The valuation program includes complete details on parameter estimation, bias correction and conservative estimation of the value of the liability under partial information. The latter is based on a new approach to the estimation of mean squared error of claims reserve prediction.

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“…Note that the bootstrapping is a general method, which can be applied to any fully defined model in order to obtain the sampling distribution for any statistic of interest. As was shown in England and Verrall (1999) and , it is straightforward to extend the bootstrapping procedure to enable an approximation to the predictive distribution to be obtained. This requires a final step to be added to the resampling method, which then simulates a future observation from the appropriate process distribution.…”

Section: Introductionmentioning

confidence: 99%

“…Note that the Schnieper method is a recursive method for claims reserving, and the appropriate background for this can be found in England and Verrall (2006). The paper by England and Verrall (1999), which first considered bootstrapping for the chain-ladder technique, was based on the over-dispersed Poisson model which is non-recursive. For ease of implementation, the detailed algorithm which can be used to obtain the bootstrap approximation to the predictive distribution for the Schnieper method is given in the Appendix.…”

Section: Introductionmentioning

confidence: 99%