Risk measures are used not only for financial institutions' internal risk management but also
for external regulation (eg, in the Basel Accord for calculating the regulatory capital …

Higher order elicitability and Osband's principle Page 1 The Annals of Statistics 2016, Vol. 44,
No. 4, 1680–1707 DOI: 10.1214/16-AOS1439 © Institute of Mathematical Statistics, 2016 …

This article reviews two leading measures of financial risk and an emerging alternative.
Embraced by the Basel accords, value-at-risk and expected shortfall are the leading …

The risk of a financial position is usually summarized by a risk measure. As this risk measure
has to be estimated from historical data, it is important to be able to verify and compare …

In the statistical and actuarial literature several generalizations of quantiles have been
considered, by means of the minimization of a suitable asymmetric loss function. All these …

Recent crises in the financial industry have shown weaknesses in the modeling of Risk-
Weighted Assets (RWAs). Relatively minor model changes may lead to substantial changes …

Informally, a statistical functional T on a set of probability measures M on the real line is
elicitable if it can be defined as the minimizer of a suitable expected scoring function. The …

In the recent Basel Accords, the expected shortfall (ES) replaces the value-at-risk (VaR) as
the standard risk measure for market risk in the banking sector, making it the most popular …

We address the problem of risk sharing among agents using a two-parameter class of
quantile-based risk measures, the so-called range-value-at-risk (RVaR), as their …

Research related to aggregation, robustness and model uncertainty of regulatory risk
measures, for instance, value-at-risk (VaR) and expected shortfall (ES), is of fundamental …