Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their … gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We … characterize loss-based risk measures by a representation theorem and give examples of such risk measures. We then discuss the …

We propose and backtest a multivariate Value-at-Risk model for financial returns based on Tukey's g-and-h distribution …-and-h distributed residuals to three European stock indices and provide results of out-of-sample Value-at-Risk backtests. We find that …

Financial risk measurement relies on models of prices and other market variables, but models inevitably rely on … finds the worst-case error in risk measurement that would be incurred through a deviation from the baseline model, given a … in a model. We apply this approach to problems of portfolio risk measurement, credit risk, delta hedging, and …

Choosing a proper external risk measure is of great regulatory importance, as exemplified in the Basel II and Basel III … Accord which use Value-at-Risk (VaR) with scenario analysis as the risk measures for setting capital requirements. We argue a … good external risk measure should be robust with respect to model misspecification and small changes in the data. A new …

The Euler (or gradient) allocation technique defines a financial institution's marginal cost of a risk exposure via … calculation of the gradient of a risk measure evaluated at the institution's current portfolio position. The technique, however …, relies on an arbitrary selection of a risk measure. We reverse the sequence of this approach by calculating the marginal …

Evaluating risk measures, premiums, and capital allocation based on dependent multi-losses is a notoriously difficult … by a heavy-tailed background risk. A particular attention is given to the distortion and weighted risk measures and … allocations, as well as their special cases such as the conditional layer expectation, tail value at risk, and the truncated tail …