The paper provides an axiomatic characterization of dynamic risk measures for multi-period financial positions. For the special case of a terminal cash flow, we require that risk depends on its conditional distribution only. We prove a representation theorem for dynamic risk measures and...

Thema der Dissertation ist zum einen die Quantifizierung und zum anderen die endogene Modellierung von Finanzrisiken. Die mathematische Analyse führt unter anderem auf Zusammenhänge finanzmathematischer Probleme mit der Theorie großer Abweichungen, der Choquet-Theorie, der Theorie...

The quantification of downside risk in terms of capital requirements is a key issue for both regulators and the financial industry. This review presents the axiomatic approach, which is based on monetary risk measures. These provide a unifying mathematical framework for the determination of...

We extend the scope of risk measures for which backtesting models are available by proposing a multinomial backtesting method for general distortion risk measures. The method relies on a stratification and randomization of risk levels. We illustrate the performance of our methods in numerical...