Loss prediction in a linear model under a linear constraint

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.

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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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Loss prediction in a linear model under a linear constraint

Cited by 3 publications

References 4 publications

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Reserve risk estimation in a linear model

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