The classical Hill estimator of a positive extreme value index (EVI) can be regarded as the logarithm of the geometric mean, or equivalently the logarithm of the mean of order p=0, of a set of adequate statistics. A simple generalisation of the Hill estimator is now proposed, considering a more...

Recurrent “black swans” financial events are a major concern for both investors and regulators because of the extreme price changes they cause, despite their very low probability of occurrence. In this paper, we use unconditional and conditional methods, such as the recently proposed high...

A class of partially reduced-bias estimators of a positive extreme value index (EVI), related to a mean-of-order-p class of EVI-estimators, is introduced and studied both asymptotically and for finite samples through a Monte-Carlo simulation study. A comparison between this class and a...

In this paper, we generalize the classical estimator of the reinsurance premium for heavy-tailed loss distributions with a kernel-type estimator. Since this estimator exhibits a bias, we propose its bias-reduced version by using a least-squares method. The asymptotic normality of the proposed...

The stable distribution, in its many parametrizations, is central to many stochastic processes. Many random variables that occur in the study of Lévy processes are related to it. Good progress has been made recently for simulating various quantities related to the stable law. In this note, we...

In finance and economics the key dynamics are often specified via stochastic differential equations (SDEs) of jump-diffusion type. The class of jump-diffusion SDEs that admits explicit solutions is rather limited. Consequently, discrete time approximations are required. In this paper we give a...

Risk assessments often encounter extreme settings with very few or no occurrences in reality.Inferences about risk indicators in such settings face the problem of insufficient data.Extreme value theory is particularly well suited for handling this type of problems.This paper uses a multivariate...

In this paper we shall be interested in two questions on extremes relating to world records in athletics.The first question is: what is the ultimate world record in a specific athletics event (such as the 100m for men or the high jump for women), given today's state of the art?Our second...

Time series of financial asset values exhibit well-known statistical features such as heavy tails and volatility clustering. We propose a nonparametric extension of the classical Peaks-Over-Threshold method from extreme value theory to fit the time varying volatility in situations where the...