It is well known that the arithmetic mean of two possibly differentcopulas forms a copula, again. More general, we focus on theweighted power mean (WPM) of two arbitrary copulas which is notnecessary a copula again, as different counterexamples reveal. However,various conditions regarding the...

The serial dependency of multivariate nancial data will often be ltered by con-sidering the residuals of univariate GARCH models adapted to every single series.This is the correct ltering strategy if the multivariate process follows a so-calledcopula based multivariate dynamic model (CMD). These...

Keynes (1911) derived general forms of probability density functions for which the “most probable value” is given by the arithmetic mean, the geometric mean, the harmonic mean, or the median. His approach was based on indirect (i.e., posterior) distributions and used a constant prior...

The serial dependency of multivariate financial data will often be filtered by considering the residuals of univariate GARCH models adapted to every single series. This is the correct filtering strategy if the multivariate process follows a so-called copula based multivariate dynamic model...

Es ist mittlerweile weitgehend unbestritten, dass der demographische Wandel eine grundlegende Reform der gesetzlichen Rentenversicherung erforderlich macht. Dies soll im Wesentlichen durch die Einführung einer Zusatzrente auf Kapitalbasis (Teilkapitaldeckungsverfahren) erfolgen. Der Beitrag...

The H−family of distributions or H−distributions, introduced by Tukey (1960, 1977), are generated by a single transformation of the standard normal distribution and allow for leptokurtosis represented by the parameter h. Alternatively, Haynes, MacGillivray and Mengersen (1997) generated...

Using the Gaussian distribution as statistical model for data sets is widely spread, especially in practice. However, departure from normality seems to be more the rule than the exception. The H-distributions, introduced by Tukey (1960, 1977), are generated by a single transformation...

Leptokurtic distributions can be generated by applying certain non-linear transformations to a standard normal random variable. Within this work we derive general conditions for these transformations which guarantee that the generated distributions are ordered with respect to the partial...