A comparison of models for the chain–ladder method

Hess, Klaus Th.; Schmidt, Klaus D.

doi:10.1016/s0167-6687(02)00160-9

Cited by 12 publications

(12 citation statements)

References 16 publications

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“…Then the expected claims of observations in occurrence year j and development year k can be estimated by (j−1) ) and H ik = H i (y ik − t ij ) − H i (y i(k−1) − t ij ) with y i(k−1) ≥ t ij , and the accumulative hazards Λ i (t) and the distribution H i (y) are defined by (2.1) and (2.4). Hence the proposed model in this paper can reproduce an aggregate data with parameterized λ 0 (t) and h 0 (t), which might be investigated in similar ways to Hess and Schmidt (2002) under the ''run-off triangle'' and the chain-ladder method, and to Mack and Venter (2000) under the assumption of the generalized linear model. However, with various effects of covariates, the proposed model with nonparametric and parametric components is more flexible.…”

Section: Discussionmentioning

confidence: 99%

Semiparametric model for prediction of individual claim loss reserving

Zhao

Zhou

Wang

2009

Insurance: Mathematics and Economics

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Section: Discussionmentioning

confidence: 99%

Semiparametric model for prediction of individual claim loss reserving

Zhao

Zhou

Wang

2009

Insurance: Mathematics and Economics

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“…In the Poisson case, the thinned claim numbers are independent, and the converse is true as well; for a proof, see Hess and Schmidt (2002).…”

Section: Corollary 33mentioning

confidence: 91%

Marginal-sum and maximum-likelihood estimation in a multiplicative tariff

Hess

2008

AStA Adv Stat Anal

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It is well known that, for a multiplicative tariff with independent Poisson distributed claim numbers in the different tariff cells, the maximum-likelihood estimators of the parameters satisfy the marginal-sum equations. In the present paper we show that this is also true under the more general assumption that the claim numbers of the different cells arise from the decomposition of a collective model for the whole portfolio of risks. In this general setting, the claim numbers of the different cells need not be independent and need not be Poisson distributed.

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“…Additional discussions regarding the model were made in Pesta and Hudecová (2012), Peters et al (2010), Schmidt (1997), andWüthrich (2008). Wüthrich and Merz (2008) also demonstrated a variety of statistical models associated with the chain-ladder method; in addition, discussions regarding model comparisons that are in terms of various aspects can be found in Mack and Ventor (2000), Verrall (2000), Hess andSchmidt (2002), andTaylor (2011). Further, a Bayesian method for an estimation of the parameters of the suggested models, which is used to derive a predictive distribution on the estimated reserve, was studied in England et al (2012), andTaylor (2015).…”

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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A comparison of models for the chain–ladder method

Cited by 12 publications

References 16 publications

Semiparametric model for prediction of individual claim loss reserving

Semiparametric model for prediction of individual claim loss reserving

Marginal-sum and maximum-likelihood estimation in a multiplicative tariff

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

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