Multivariate loss prediction in the multivariate additive model

Hess, Klaus Th.; Schmidt, Klaus D.; Zocher, Mathias

doi:10.1016/j.insmatheco.2006.02.004

Cited by 24 publications

(15 citation statements)

References 8 publications

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“…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. These results have been completed and extended by Ludwig et al (2009); see Sects.…”

Section: Multivariate Stochastic Modelsmentioning

confidence: 99%

“…The multivariate additive model was introduced and studied byHess et al (2006) under a slightly more general assumption on the matrices V i . 28 The computations are straightforward; seeLudwig et al (2009) for cumulative losses and all reserves,Merz and Wüthrich (2009a) for the accident year reserves and the total reserve, andLudwig and Schmidt (2010b) for the calendar year reserves.…”

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confidence: 99%

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Loss prediction based on run-off triangles

Schmidt

2011

AStA Adv Stat Anal

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Section: Multivariate Stochastic Modelsmentioning

confidence: 99%

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confidence: 99%

Loss prediction based on run-off triangles

Schmidt

2011

AStA Adv Stat Anal

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“…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%

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

2010

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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.

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“…The problem is to predict -the non-observable incremental losses Z i,k with i + k ≥ n + 1 2 For a linear model leading to the general multivariate additive method for an arbitrary number of correlated portfolios of risks, see Hess et al (2006). 3 Another approach to reduce the gap between the predictors of paid and incurred ultimate losses was recently proposed by Quarg and Mack (2004), who proposed a model related to the chain-ladder method.…”

Section: The Univariate Additive Model Of Loss Reservingmentioning

confidence: 99%

“…This model is said to be bivariate since it applies to two portfolios of risks; see Hess et al (2006) for the multivariate additive model with a general correlation structure.…”

Section: The Bivariate Additive Model Of Loss Reservingmentioning

confidence: 99%

Loss prediction in a linear model under a linear constraint

Kloberdanz

Schmidt

2008

AStA Adv Stat Anal

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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.In the present paper we study conjoint prediction of paid and incurred losses in a linear model with a linear constraint which is intended to reduce the gap between the predictors of ultimate paid and incurred losses. We thus present an application to actuarial mathematics of the general result established by Kloberdanz and Schmidt (AStA Adv. Stat. Anal. 92:207-215, 2008).

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Multivariate loss prediction in the multivariate additive model

Cited by 24 publications

References 8 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

Loss prediction in a linear model under a linear constraint

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