Addendum to ‘The multi-year non-life insurance risk in the additive reserving model’ [Insurance Math. Econom. 52(3) (2013) 590–598]: Quantification of multi-year non-life insurance risk in chain ladder reserving models

Diers, Dorothea; Linde, Marc; Hahn, Lukas Josef

doi:10.1016/j.insmatheco.2015.10.013

Cited by 13 publications

(6 citation statements)

References 10 publications

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“…(2006), Diers et al . (2016), Lindholm et al . (2020), one could Taylor approximate the estimation error part of the MSEP calculation directly, making use of the Hessian from the QMLE-fitting.…”

Section: Estimationmentioning

confidence: 99%

A Collective Reserving Model With Claim Openness

Lindholm¹,

Zakrisson²

2021

ASTIN Bull.

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The present paper introduces a simple aggregated reserving model based on claim count and payment dynamics, which allows for claim closings and re-openings. The modelling starts off from individual Poisson process claim dynamics in discrete time, keeping track of accident year, reporting year and payment delay. This modelling approach is closely related to the one underpinning the so-called double chain-ladder model, and it allows for producing separate reported but not settled and incurred but not reported reserves. Even though the introduction of claim closings and re-openings will produce new types of dependencies, it is possible to use flexible parametrisations in terms of, for example, generalised linear models (GLM) whose parameters can be estimated based on aggregated data using quasi-likelihood theory. Moreover, it is possible to obtain interpretable and explicit moment calculations, as well as having consistency of normalised reserves when the number of contracts tend to infinity. Further, by having access to simple analytic expressions for moments, it is computationally cheap to bootstrap the mean squared error of prediction for reserves. The performance of the model is illustrated using a flexible GLM parametrisation evaluated on non-trivial simulated claims data. This numerical illustration indicates a clear improvement compared with models not taking claim closings and re-openings into account. The results are also seen to be of comparable quality with machine learning models for aggregated data not taking claim openness into account.

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Section: Estimationmentioning

confidence: 99%

A Collective Reserving Model With Claim Openness

Lindholm¹,

Zakrisson²

2021

ASTIN Bull.

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“…A number of papers have derived the same estimator based on different approaches to statistical estimation in settings consistent with the distribution-free chain ladder, see for example Merz and Wüthrich (2008), Röhr (2016), Diers et al . (2016), Gisler (2019), and Lindholm et al . (2020).…”

Section: Introductionmentioning

confidence: 97%

“…The key contribution is the estimator of the contribution of parameter estimation error to conditional mean squared error of prediction. A number of papers have derived the same estimator based on different approaches to statistical estimation in settings consistent with the distribution-free chain ladder, see for example Merz and Wüthrich (2008), Röhr (2016), Diers et al (2016), Gisler (2019), and Lindholm et al (2020).…”

Section: Introductionmentioning

confidence: 99%

Mack’s estimator motivated by large exposure asymptotics in a compound poisson setting

Engler,

Lindskog

2024

ASTIN Bull.

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The distribution-free chain ladder of Mack justified the use of the chain ladder predictor and enabled Mack to derive an estimator of conditional mean squared error of prediction for the chain ladder predictor. Classical insurance loss models, that is of compound Poisson type, are not consistent with Mack’s distribution-free chain ladder. However, for a sequence of compound Poisson loss models indexed by exposure (e.g., number of contracts), we show that the chain ladder predictor and Mack’s estimator of conditional mean squared error of prediction can be derived by considering large exposure asymptotics. Hence, quantifying chain ladder prediction uncertainty can be done with Mack’s estimator without relying on the validity of the model assumptions of the distribution-free chain ladder.

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“…Subsequent influential research has focused on revisiting the proposed prediction errors. For example, Diers et al (2016) estimate the prediction error using bootstrap techniques. Röhr (2016) rewrites the prediction error of ultimate run-off risks as a function of the individual future CL DFs.…”

Section: Introductionmentioning

confidence: 99%

A semi-parametric claims reserving model with monotone splines

Chang,

Gao,

Shi

2024

Ann Oper Res

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Stochastic reserving models used in the insurance industry are usually based on an assumed distribution of claim amounts. Despite their popularity, such models may unavoidably be affected by the misspecification issue given that it is likely that the underlying distribution will be different from that assumed. In this paper, we incorporate monotone splines to ensure the expected monotonically increasing pattern of cumulative development factors (CDFs) to develop a new semi-parametric reserving model that does not require a density assumption. To allow the maximum utilization of available information, we also propose an enhanced sampling approach that greatly increases the size of unbiased CDFs, particularly in later development periods. Based on the enhanced samples, a bootstrap technique is employed in the estimation of monotone splines, from which incurred-but-not-reported (IBNR) reserves and prediction errors can be obtained. Associated technical features, such as the consistency of estimator, are discussed and demonstrated. Our simulation studies suggest that the new model improves the accuracy of IBNR reserving, compared with a range of classic competing models. A real data analysis produces many consistent findings, thus supporting the usefulness of the monotone spline model in actuarial and insurance practice.

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Addendum to ‘The multi-year non-life insurance risk in the additive reserving model’ [Insurance Math. Econom. 52(3) (2013) 590–598]: Quantification of multi-year non-life insurance risk in chain ladder reserving models

Cited by 13 publications

References 10 publications

A Collective Reserving Model With Claim Openness

A Collective Reserving Model With Claim Openness

Mack’s estimator motivated by large exposure asymptotics in a compound poisson setting

A semi-parametric claims reserving model with monotone splines

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