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| 4 avril 2014
Extreme value statistics for truncated Pareto type distributions
Jan Beirlant (K.U. Leuven, Belgium)
14:00-15:00, salle Internef 123
Aban, Meerschaert and Panorska (2006) derived the maximum likelihood estimator for the tail index of a truncated Pareto distribution with right truncation point T. They discuss and compare the use of the Hill (1975) and the maximum likelihood estimator under truncation in some practical settings. The Hill estimator is then considered as a limit case by letting T to infinity. The problem of extreme value es- timation under (right) truncation was also introduced in Nuyts (2010) who proposed a similar estimator for the tail index, extending the estimator from Aban et al. (2006) introducing trimming of the number of extreme order statistics. Clark (2013) discusses such estimation problems from a risk management perspective. Given that in practice one does not always know if the distribution is truncated or not, we study the properties of the estimators introduced in these papers in case of the general class of Pareto-type distributions, both truncated and not truncated (T to infinity). We also consider the effect of trimming and study the estimation of extreme quantiles within this setting. Finally we conclude with simulation results and discuss some practical examples.
|28 avril 2014
Risk Measures within a Credibility Framework
Georgios Pitselis (University of Piraeus, Greece and K.U. Leuven, Belgium)
11:00-12:00, salle Extranef 125
In the insurance and financial industry there are cases where different firms have similar but not identical risks. In this paper we introduce new risk measures called credible risk measures in order to recapture the risk of an individual insurer's contract (or financial sector) as well as the industry risk. Some of these measures are: the credible value at risk (CrVaR), the credible conditional tail expectation (CrCTE), the credible tail conditional median (CrTCM) and the credible quantile tail expectation (CrQTE). Credible risk measures provide more complete tools than the usual risk measures (i.e. VaR, CTE) in capturing the individual insurer's risk and industry's risk. The advantages of these new credible measures in comparison with the existing risk measures are also presented.
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