This paper studies properties and applications related to the mixture of the class of distributions built by the Lehmann's alternative (also referred to in the statistical literature as max-stable or exponentiated distribution) of the form [𝐺(·)]𝜆, where 𝜆0 and 𝐺(·) is a continuous...

Under the revised market risk framework of the Basel Committee on Banking Supervision, the model validation regime for internal models now requires that models capture the tail risk in profit-and-loss (P&L) distributions at the trading desk level. We develop multi-desk backtests, which...

In the broader landscape of cryptocurrency risk management, this study delves into the nuanced estimation of Value-at-Risk (VaR) for a uniformly weighted portfolio of cryptocurrencies, employing the bivariate Normal Inverse Gaussian distribution renowned for its semi-heavy tails. Utilizing...

Numerous robust estimators exist as alternatives to the maximum likelihood estimator (MLE) when a completely observed ground-up loss severity sample dataset is available. However, the options for robust alternatives to a MLE become significantly limited when dealing with grouped loss severity...

This study investigates the simplicity and adequacy of tail-based risk measures-valueat-risk (VaR) and expected shortfall (ES)-when applied to tail targeting of the extreme value (EV) model. We implement Lévy-VaR and ES risk measures as full density-based alternatives to the generalized Pareto...