We describe characteristics of various risk measures (Value-at-Risk, Expected Shortfall, etc.) that are used to analyze … and quantify the tail risk exposure, and discuss their relative strengths and weaknesses. Emphasis is placed on presenting … and comparing methodologies to compute and backtest estimates for these risk measures, from a practical perspective. We …

asymptotic distribution can easily be derived. A simulation study confirms that the modified estimator works well. …

implement. The modified estimator is still pn{consistent and we derive its asymptotic distribution. A simulation study confirms …

Matching estimators are widely used in statistical data analysis. However, the distribution of matching estimators has … matching estimators. This representation allows the use of martingale limit theorems to derive the asymptotic distribution of … matching estimators. As an illustration of the applicability of the theory, we derive the asymptotic distribution of a matching …

-series. Available models suffer from the curse of dimensionality or restrictive assumptions on the parameters and the distribution. A …