Estimation of IBNR claims by credibility theory

Devylder, F.

doi:10.1016/0167-6687(82)90019-1

Cited by 20 publications

(4 citation statements)

References 4 publications

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“…By modelling that we could complement the point forecasts with distribution forecasts. Recently, Harnau and Nielsen (2018) developed an asymptotic distribution theory for the chain ladder within an over-dispersed Poisson framework. The present situation is a special case of their setup so it could potentially be extended with Bornhuetter-Ferguson adjustments.…”

Section: Discussionmentioning

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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Section: Discussionmentioning

confidence: 99%

A Likelihood Approach to Bornhuetter–Ferguson Analysis

Elpidorou

Margraf

Martínez-Miranda

et al. 2019

Risks

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“…(1979) [2] ，其中有些保费原理可以看做是某类损失函数下风险的最优估计。Gerber (1980) [3] 文章中定义了加权损失函数，注意到在损失函数的范围中，Furman et al [4] 的广义加权保费原理，在 Herff et al [5] 提出类似保费， Kamps [6] 提出定义及研究了相关的性质。后在各类保费原理的模型下都有涉及 Kamp 保费原理，其研究一般类似于 Esscher 保费原理，如 K. D. Schmidt et al [7] 以及 M. Pan et al [8] 讨论了这方面的情形。在保险的实际运用中，由于风险随机变量 X 的分布是未知的，因此保费也是未知的。但我们可能已经对损失有了多次观测，我们把这些观测看做风险随机变量的一个样本。因此根据样本和相关的风险特征信息对保费进行合适的估计，并作出进行相应的统计推断，即可应用于责任准备金，可参考 Vylder [9] ，巨额风险，奖惩系统，死亡率等领域中。 [5] )，…”

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Nonparametric Estimation of Kamp Premium Principle

熊¹

2013

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Based on the generalized weighted premium, this paper gives a brief introduction on Kamp premium principle. Through the establishment of Bayesian theory model, a set of samples is given to assume that parameters have a prior distribution. Then the Bayesian formula is used to calculate the posterior mean value. We make Bayesian estimation and linear Bayesian estimation on the Kamp premium principle, and get the credibility estimation of Kamp premium principle after analyzing the approximate of parameters under above conditions. At the same time, we prove the asymptotic of this estimation. Finally, the convergence of the provided estimates is tested by the numerical simulation.

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“…The resulting model is a two-stage hierarchical regression model with random coefficients, where the first and second stage correspond to type of claims and exposure periods, respectively. Also De Vylder (1982), Norberg (1986a) and Witting (1987) model varying risk conditions by means of random parameters in an empirical Bayes setting. Somewhat related are the works by Jewell (1989Jewell ( , 1990a.…”

Section: Introductionmentioning

confidence: 99%

Prediction of Outstanding Claims: A Hierarchical Credibility Approach

Hesselager¹

1991

Scandinavian Actuarial Journal

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O. Prediction of outstanding claims: A hierarchical credibility approach. Scand. Actuarial J. 1991; 1: 25-47.We consider the problem of predicting unpaid losses in respect of incurred, but not yet reported claims in the case where the distribution of delays until notification may depend on the type of claim. A hierarchical credibility model is presented, where the distribution of delays corresponding to different types of claims, as well as other characteristics affecting the claims experience, are viewed as realizations of unobservable random variables. The proposed method is illustrated by a numerical example.

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Estimation of IBNR claims by credibility theory

Cited by 20 publications

References 4 publications

A Likelihood Approach to Bornhuetter–Ferguson Analysis

A Likelihood Approach to Bornhuetter–Ferguson Analysis

Nonparametric Estimation of Kamp Premium Principle

Prediction of Outstanding Claims: A Hierarchical Credibility Approach

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