Various Faces of Risk Measures: Internal Model's Perspective

In this article, we consider several aspects of risk measures from the internal models’ perspective. We critically review the most widely used classes of risk measures. Especially, we attempt to clear up some of the most commonly misconstructed aspects: the choice between risk measures, and practical data and forecasting issues, like the importance of robustness. As a new result, solvency capital requirement is optimized under variance premium principle. The use of tail conditional trimmed mean is proposed as a robust risk estimator. One objective of this article is to emphasize that one single risk measure or a specific axiomatic system is not appropriate for all purposes.