Numerical evaluation of compound distributions is an important task in insurance mathematics and quantitative risk management. In practice, both recursive methods as well as transform based techniques are widely used. We give a survey of these tools, point out the respective merits and provide...

A generic algorithmic framework for nonlinear ensemble filtering based on Gaussian mixtures and fuzzy clustering techniques is introduced. The framework generalizes the ensemble Kalman filter and relaxes the assumption of a Gaussian prediction distribution. A theoretical analysis of the proposed...

Mainly due to new capital adequacy standards for banking and insurance, an increased interest exists in the aggregation properties of risk measures like Value-at-Risk (VaR). We show how VaR can change from sub to superadditivity depending on the properties of the underlying model. Mainly, the...

Motivated by too restrictive or even incorrect statements about generalized inverses in the literature, properties about these functions are investigated and proven. Examples and counterexamples show the importance of generalized inverses in mathematical theory and its applications. Copyright...

Motivated by too restrictive or even incorrect statements about generalized inverses in the literature, properties about these functions are investigated and proven. Examples and counterexamples show the importance of generalized inverses in mathematical theory and its applications. Copyright...