We use a subsample bootstrap method to get a consistent estimate of the asymptotically optimal choice of the samplefraction, in the sense of minimal mean squared error, which is needed for tail index estimation. Unlike previous methodsour procedure is fully self contained. In particular, the...

Accurate prediction of the frequency of extreme events is of primary importance in many financialapplications such as Value-at-Risk (VaR) analysis. We propose a semi-parametric method for VaRevaluation. The largest risks are modelled parametrically, while smaller risks are captured by the...

Economic problems such as large claims analysis in insurance and value-at-risk in finance, requireassessment of the probability P of extreme realizations Q. This paper provided a semi-parametricmethod for estimation of extreme (P, Q) combinations for data with heavy tails. We solve the...