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...

The interdependence between multiple lines of business has an important impact on determining loss reserves and risk capital, which are crucial for the solvency of a property and casualty (P&C) insurance company. In this work, we introduce the two-stage inference method using the Sarmanov family...

In this research, we employ a full-range tail dependence copula to capture the intraday dynamic tail dependence patterns of 30 s log returns among stocks in the US market in the year of 2020, when the market experienced a significant sell-off and a rally thereafter. We also introduce a...

Log-concavity and log-convexity play a key role in various scientific fields, especially in those where the distinction between exponential and non-exponential distributions is necessary for inferential purposes. In the present study, we introduce a testing procedure for the tail part of a...

Constructing an accurate model for insurance losses is a challenging task. Researchers have developed various methods to model insurance losses, such as composite models. Composite models combine two distributions: one for part of the data with small and high frequencies and the other for large...

In this article, we study stochastic orders over an interval. Mainly, we focus on orders related to the Laplace transform. The results are then applied to obtain a bound for heavy-tailed distributions and are illustrated by some examples. We also indicate how these ordering relationships can be...

The Danish fire loss dataset records commercial fire losses under three insurance coverages: building, contents, and profits. Existing research has primarily focused on the heavy-tail behaviour of the losses but ignored the relationship among different insurance coverages. In this paper, we aim...

This paper seeks to identify computationally efficient importance sampling (IS) algorithms for estimating large deviation probabilities for the loss on a portfolio of loans. Related literature typically assumes that realised losses on defaulted loans can be predicted with certainty, i.e., that...