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...

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...