The Prediction Error of the Chain Ladder Method Applied to Correlated Run-off Triangles

Braun, Christian

doi:10.2143/ast.34.2.505150

Cited by 36 publications

(43 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It extends the bivariate model proposed by Braun (2004) who used it not for prediction but only for developing estimators of the mean squared error of prediction of the ultimate losses of a portfolio consisting of two lines of business. 32 This was first pointed out by Ajne (1994) for the chain-ladder method; see also Schmidt (2006b).…”

Section: Bivariate Gauss-markov Prediction For Paid and Incurred Lossesmentioning

confidence: 96%

“…32 This was first pointed out by Ajne (1994) for the chain-ladder method; see also Schmidt (2006b). 33 Braun (2004) wrote: The aggregation of run-off triangles with different development patterns is like mixing apples and oranges and will normally lead to invalid results.…”

Section: Bivariate Gauss-markov Prediction For Paid and Incurred Lossesmentioning

confidence: 99%

“…Although this problem had been addressed before by Halliwell (1997), it was their paper which was widely recognized. In the same year, Braun (2004) introduced the bivariate chain-ladder model with the aim of improving not the predictors but the approximation of the mean squared error of prediction for the sum of two lines of business. Inspired by the model of Braun (2004), Pröhl and Schmidt (2005) and Hess et al (2006) proposed Gauss-Markov prediction in multivariate extensions of the chainladder model and the additive model, respectively.…”

Section: Multivariate Stochastic Modelsmentioning

confidence: 99%

See 2 more Smart Citations

Loss prediction based on run-off triangles

Schmidt

2011

AStA Adv Stat Anal

View full text Add to dashboard Cite

Loss reserving is an important subject of actuarial mathematics. It aims at the prediction of future losses caused by claims which have incurred in the past but have not yet been closed. The problem of predicting such losses is particularly important in liability insurance. More generally, it is most relevant with respect to the new regulatory requirements for insurance companies operating in the European Union, which are known as Solvency II.

show abstract

Section: Bivariate Gauss-markov Prediction For Paid and Incurred Lossesmentioning

confidence: 96%

Section: Bivariate Gauss-markov Prediction For Paid and Incurred Lossesmentioning

confidence: 99%

Section: Multivariate Stochastic Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Loss prediction based on run-off triangles

Schmidt

2011

AStA Adv Stat Anal

View full text Add to dashboard Cite

show abstract

“…In the literature claims reserving methods for portfolios of several correlated run-off portfolios have been studied by Braun (2004), Schmidt (2006aSchmidt ( , 2006b, Pröhl and Schmidt (2005), Mildenhall (2006), Hess et al (2006), Hürlimann (2005) and Merz and Wüthrich (2008a, 2008b, 2008c. Simulation based approaches which extend the bootstrapping technique from a single run-off portfolio to several correlated run-off portfolios are given by Brehm (2002), Kirschner et al (2002) and Taylor andMcGuire (2005, 2007).…”

Section: Claims Reserving For Several Correlated Run-off Portfoliosmentioning

confidence: 99%

“…• Within the CL framework for several correlated run-off portfolios Braun (2004) and Wüthrich (2008a, 2007) proposed the development year-based correlations given by (10). Often correlations between different run-off triangles are attributed to claims inflation.…”

Section: Remarks 22mentioning

confidence: 99%

Bootstrapping the chain-ladder method for several correlated run-off portfolios

2010

View full text Add to dashboard Cite

The prediction of the outstanding loss liabilities for a non-life run-off portfolio as well as the quantification of the prediction error is one of the most important actuarial tasks in non-life insurance. In this paper we consider this prediction problem in a multivariate context. More precisely, we derive the predictive distribution of the claims reserves simultaneously for several correlated run-off portfolios in the framework of the Chain-ladder claims reserving method for several correlated run-off portfolios.Zusammenfassung Die Prognose der noch ausstehenden Schadenaufwendungen und die Quantifizierung des damit verbundenen Prognosefehlers ist für NichtlebenVersicherer von großer Bedeutung. In der vorliegenden Arbeit wird die prädiktive Verteilung für die Schadenreserve mehrerer korrelierter Run-Off-Portfolios mittels Bootstrapping im Rahmen eines multivariaten Chain-Ladder-Reservierungsverfahrens berechnet. Die Betrachtung mehrerer korrelierter Run-Off-Portfolios ist vor allem dadurch motiviert, dass es in der Praxis der Schadenreservierung häufig notwendig ist, ein gegebenes Run-Off-Portfolio erst in mehrere (Sub-) Run-Off-Portfolios zu zerlegen, bevor die für eine sinnvolle Anwendung des verwendeten Schadenreservierungsverfahren notwendigen Homogenitätseigenschaften zumindest ansatzweise erfüllt sind.

show abstract

Bibliography

2012

Stochastic Claims Reserving Methods in Insurance

View full text Add to dashboard Cite

The Prediction Error of the Chain Ladder Method Applied to Correlated Run-off Triangles

Abstract: It is shown how the distribution-free method of Mack (1993) can be extended in order to estimate the prediction error of the Chain Ladder method for a portfolio of several correlated run-off triangles.

Cited by 36 publications

References 3 publications

Loss prediction based on run-off triangles

Loss prediction based on run-off triangles

Bootstrapping the chain-ladder method for several correlated run-off portfolios

Bibliography

Contact Info

Product

Resources

About