While modern portfolio theory grounds on the trade-off between portfolio return and portfolio variance to determine the optimal investment decision, postmodern portfolio theory uses downside risk measures instead of the variance. Prominent examples are given by the risk measures Value-at-Risk...

Quantifying risk is pivotal for every financial institution. In the conventional framework, time is the key aspect for all the well-established risk measures. However, extracting and analyzing the frequency information conveyed by financial data, could yield improved insights about the inherent...

We use influence functions as a basic tool to study unconditional non-parametric and parametric expected shortfall (ES) estimators with regard to returns data influence, standard errors and coherence. Non-parametric ES estimators have a monotonically decreasing influence function of returns. ES...