Denote the loss return on the equity of a financial institution as X and that of the entire market as Y . For a given very small value of p 0, the marginal expected shortfall (MES) is defined as E(X | Y QY (1−p)), where QY (1−p) is the (1−p)-th quantile of the distribution of Y . The MES...

We extend classical extreme value theory to non-identically distributed observations. When the distribution tails are proportional much of extreme value statistics remains valid. The proportionality function for the tails can be estimated nonparametrically along with the (common) extreme value...

When simultaneously monitoring two possibly dependent, positive risks one is often interested in quantile regions with very small probability p. These extreme quantile regions contain hardly or no data and therefore statistical inference is difficult. In particular when we want to protect...

There is no scientific consensus on the fundamental question whether the probability distribution of the human life span has a finite endpoint or not and, if so, whether this upper limit changes over time. Our study uses a unique dataset of the ages at death - in days - of all (about 285,000)...