A credibility approach to the munich chain-ladder method

Merz, Michael; Wüthrich, Mario V.

doi:10.1007/bf02809220

Cited by 11 publications

(9 citation statements)

References 6 publications

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“…The basic idea behind the Munich chain-ladder method is to consider best predictions based on both sets of information B j = B P j ∪ B I j , that is, how does prediction of, say, cumulative payments P i,j+1 improve by enlarging the information from B P j to B j . This is similar to the considerations in [3]. In this section, we start with the special case of "one-step ahead prediction", the general case is presented in Section 6, below.…”

Section: One-step Ahead Predictionmentioning

confidence: 70%

Modified Munich Chain-Ladder Method

Merz

Wüthrich

2015

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Section: One-step Ahead Predictionmentioning

confidence: 70%

Modified Munich Chain-Ladder Method

Merz

Wüthrich

2015

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“…, that is, how does prediction of, say, cumulative payments P i,j+1 improve by enlarging the information from B P j to B j . This is similar to the considerations in [3]. In this section, we start with the special case of "one-step ahead prediction", the general case is presented in Section 6, below.…”

Section: Chain-ladder Modelsmentioning

confidence: 70%

“…In Theorem 4.1 of [3], the Munich chain-ladder structure has been found as a best linear approximation to E [P i,j+1 | B j ] in the following way…”

Section: With Non-identical Weights)mentioning

confidence: 99%

“…The first way is to define a stochastic model which has the required structure of the Munich chain-ladder factors; this is the approach taken in [1]. The second way is to define a general chain-ladder model and to derive estimators in this model that have the Munich chain-ladder factor structure; this is the approach taken in [3]. Here, we analyze both of these views and we show how the second way leads to a modified Munich chain-ladder method.…”

Section: Introductionmentioning

confidence: 99%

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Modified Munich Chain-Ladder Method

Merz

Wüthrich

2014

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract: The Munich chain-ladder method for claims reserving was introduced by Quarg and Mack on an axiomatic basis. We analyze these axioms, and we define a modified Munich chain-ladder method which is based on an explicit stochastic model. This stochastic model then allows us to consider claims prediction and prediction uncertainty for the Munich chain-ladder method in a consistent way. Terms of use: Documents in EconStor may

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“…We also provide standard errors of prediction for the reserves obtained by this approach. Another approach to solve the paid/incurred problem, the so-called Munich chain-ladder model, was developed by Quarg and Mack (2004) and further motivated by Merz and Wüthrich (2006). However, volatilities of reserve predictors in the Munich chain-ladder model still have to be derived.…”

Section: Introductionmentioning

confidence: 98%

Reserve risk estimation in a linear model

Ludwig¹,

Schmeißer²,

Thänert

2011

ZVersWiss

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This paper presents the linear model, a framework for stochastic modeling of known methods as well as for the development of new methods of loss reserving. The linear model allows the determination of optimal predictors of non-observable cumulated and incremental losses and thus the derivation of optimal reserves by minimization of the expected squared prediction error.This paper embeds the model of Panning (Measuring loss reserve uncertainty. CAS Forum, Fall 2006, pp. 237-267, 2006 into the context of linear models, extents it to the multivariate case and describes an application of the model of Panning to solve the paid/incurred-problem. In all cases the computation of volatilities of reserve predictors and of the claims development result relevant for Solvency II is possible.Zusammenfassung In diesem Aufsatz wird das Lineare Modell als Rahmenkonzeption zur stochastischen Modellierung bekannter und zur Entwicklung neuer Verfahren der Schadenreservierung dargestellt. Das Lineare Modell gestattet die Bestimmung optimaler Prädiktoren für nicht-beobachtbare Schadenstände und -zuwächse und damit die Bestimmung optimaler Reserven durch die Minimierung des erwarteten quadratischen Prognosefehlers.Dieser Aufsatz bettet das Modell von Panning (Measuring loss reserve uncertainty. CAS Forum, Fall 2006, pp. 237-267, 2006 in den Kontext Linearer Modelle ein, A. Ludwig ( ) zeb/rolfes.schierenbeck.associates, Hammer Straße 165, A. Ludwig et al. erweitert dieses auf den multivariaten Fall und beschreibt eine Anwendung des Modells von Panning zur Lösung des Paid/Incurred-Problems. In allen Fällen ist eine Berechnung von Volatilitäten von Reserveprädiktoren sowie des Solvency II-relevanten Claims Development Result möglich.

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A credibility approach to the munich chain-ladder method

Cited by 11 publications

References 6 publications

Modified Munich Chain-Ladder Method

Modified Munich Chain-Ladder Method

Modified Munich Chain-Ladder Method

Reserve risk estimation in a linear model

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