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Mainly due to new capital adequacy standards for banking and insurance, an increased interest exists in the aggregation properties of risk measures like Value-atRisk (VaR). We show how VaR can change from subto superadditivity depending on the properties of the underlying model. Mainly, the switch from a finite to an infinite mean model gives a completely… (More)

- Paul Embrechts, Dominik D. Lambrigger, Mario V. Wüthrich
- 2008

Properties of risk measures for extreme risks have become an important topic of research. In the present paper we discuss suband superadditivity of quantile based risk measures and show how multivariate extreme value theory yields the ideal modeling environment. Numerous examples and counter-examples highlight the applicability of the main results obtained.

- Mario V. Wüthrich, Massimo De Felice, Alois Gisler
- 2008

We assume that the claims liability process satisfies the distribution-free chainladder model assumptions. For claims reserving at time I we predict the total ultimate claim with the information available at time I and, similarly, at time I + 1 we predict the same total ultimate claim with the (updated) information available at time I +1. The claims… (More)

We prove a two-dimensional version of the famous Pickands–Balkema–de Haan theorem of extreme value theory. The bivariate random variables are generated using the copula language. This representation of dependence structures allows to derive asymptotic results for bivariate excess distributions. 2003 Elsevier SAS. All rights reserved. Résumé Une version en… (More)

- Markus Buchwalder, Michael Merz, Hans Bühlmann, Mario V. Wüthrich
- 2005

We study the Legal Valuation Portfolio (VaPo) for the runoff of a non-life insurance company. Therefore we introduce financial instruments as basis elements to value the single runoff payments (cash flows). Since from a regulatory point of view it is not sufficient to just have best-estimates reserves we consider in addition a risk-adjusted margin to… (More)

We consider the chain ladder reserving method in a Bayesian set up, which allows for combining individual claims development data with portfolio information as for instance development patterns from industry-wide data. We derive the Bayes estimators and the credibility estimators within this Bayesian framework. We show that the credibility estimators are… (More)

- Hans Bühlmann, Massimo De Felice, Alois Gisler, Franco Moriconi, Mario V. Wüthrich
- 2008

In recent Solvency II considerations much effort has been put into the development of appropriate models for the study of the one-year loss reserving uncertainty in non-life insurance. In this article we derive formulas for the conditional mean square error of prediction of the one-year claims development result in the context of the Bayes chain ladder… (More)

In the present paper we consider the claims reserving problem in a multivariate context, that is, we study the multivariate Chain-ladder (CL) method for a portfolio of N correlated run-off triangles based on multivariate age-to-age factors. This method allows for a simultaneous study of individual run-off subportfolios and facilitates the derivation of an… (More)

The intention of this paper is to analyse the mean square error of prediction (MSEP) under the distribution-free chain ladder (DFCL) claims reserving method. We compare the estimation obtained from the classical bootstrap method with the one obtained from a Bayesian bootstrap. To achieve this in the DFCL model we develop a novel approximate Bayesian… (More)

Using the distribution-free chain ladder method, we estimate the total ultimate claim amounts at time I, and after updating the information, at time I 1. The observable claims development result at time I 1 for accounting year (I, I 1] is then defined to be the difference between these two successive best estimate predictions for the ultimate claim. We… (More)