Einführung in die Welt der Mathematik, die sich bemüht, die Idee der mathematischen Konzepte verständlich zu machen. Ziel ist es, den Mathematik-Schein leichter erwerben zu können - und das mit nachhaltigem Nutzen für das weitere Studium. -- I Grundlagen. Logik. Mengen und Abbildungen. --...

We consider the problem of calculating tail probabilities of the returns of linear asset portfolios. As a flexible and accurate model for the logarithmic returns we use the t-copula dependence structure and marginals following the generalized hyperbolic distribution. Exact calculation of the...

It is well known that for highly skewed distributions the standard method of using the t statistic for the confidence interval of the mean does not give robust results. This is an important problem for importance sampling (IS) as its final distribution is often skewed due to a heavy tailed...

The inversion method for generating non-uniformly distributed random variates is a crucial part in many applications of Monte Carlo techniques, e.g., when low discrepancy sequences or copula based models are used. Unfortunately, closed form expressions of quantile functions of important...

There exists a vast literature on nonuniform random variate generators. Most of these generators are especially designed for a particular distribution. However, in pratice only a few of these are available to practioners. Moreover, for problems as (e.g.) sampling from the truncated normal...