Value at Risk (VaR) is the most popular market risk measure as it summarizes in one figure the exposure to different risk factors. It had been around for over a decade when Expected Shortfall (ES) emerged to correct its shortcomings. Both risk measures can be estimated under several models. We...

This paper develops an approach based on Gram-Charlier-like expansions for modeling financial series to take in due account features such as leptokurtosis. A Gram-Charlier-like expansion adjusts the moments of interest of a given distribution via its own orthogonal polynomials. This approach,...

The paper develops a tail risk forecasting model that incorporates the wealth of economic and financial information available to risk managers. The approach can be viewed as a regularized extension of the two-stage GARCH-EVT model of McNeil and Frey (2000) where we permit a time-varying...

A simple and commonly used method to approximate the total claim distribution of a (possible weakly dependent) insurance collective is the normal approximation. In this article, we investigate the error made when the normal approximation is plugged in a fairly general distribution-invariant risk...

In optimization problems appearing in fields such as economics, finance, or engineering, it is often important that a risk measure of a decision-dependent random variable stays below a prescribed level. At the same time, the underlying probability distribution determining the risk measure's...

Robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is of crucial importance when making well-informed risk management decisions. In this paper, we quantify for any given distortion risk measure its robustness to distributional uncertainty by...

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...