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Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation…
This paper studies properties of functions having monotone tails. We extend Theorem 1 of Dhaene et al. (2002a) and show how the tail quantiles of a random variable transformed with a monotone tail function can be expressed as the…
Risk assessment for rare events is essential for understanding systemic stability in complex systems. As rare events are typically highly correlated, it is important to study heavy-tailed multivariate distributions of the relevant…
We consider risk-neutral returns and show how their tail asymptotics translate directly to asymptotics of the implied volatility smile, thereby sharpening Roger Lee's celebrated moment formula. The theory of regular variation provides the…
We establish a statistical learning theoretical framework aimed at extrapolation, or out-of-domain generalization, on the unobserved tails of covariates in continuous regression problems. Our strategy involves performing statistical…
In this paper, we compute multivariate tail risk probabilities where the marginal risks are heavy-tailed and the dependence structure is a Gaussian copula. The marginal heavy-tailed risks are modeled using regular variation which leads to a…
Gaussian random vectors exhibit the loss of dimension phenomena, which relate to their joint survival tail behaviour. Besides, the fact that the components of such vectors are light-tailed complicates the approximations of various…
Tail risk protection is in the focus of the financial industry and requires solid mathematical and statistical tools, especially when a trading strategy is derived. Recent hype driven by machine learning (ML) mechanisms has raised the…
Random deflated risk models have been considered in recent literatures. In this paper, we investigate second-order tail behavior of the deflated risk X=RS under the assumptions of second-order regular variation on the survival functions of…
Regular and rapid variation have been extensively studied in the literature and applied across various fields, particularly in extreme value theory. In this paper, we examine regular and rapid variation through the lens of generalized…
Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…
In risk management, tail risks are of crucial importance. The assessment of risks should be carried out in accordance with the regulatory authority's requirement at high quantiles. In general, the underlying distribution function is…
The upper extremes of a Markov chain with regulary varying stationary marginal distribution are known to exhibit under general conditions a multiplicative random walk structure called the tail chain. More generally, if the Markov chain is…
For a risk vector $V$, whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents' exposure risk and the aggregated risk in the market. Risk is measured by…
Assessing the probability of occurrence of extreme events is a crucial issue in various fields like finance, insurance, telecommunication or environmental sciences. In a multivariate framework, the tail dependence is characterized by the…
We consider random vectors $X$ that satisfy the equation in law $X=AX+B$, where $A$ is a given random diagonal matrix and $B$ a given random vector, both independent of $X$. It is well known by the works of Kesten and Goldie that the…
For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…
Probabilistic forecasts comprehensively describe the uncertainty in the unknown future outcome, making them essential for decision making and risk management. While several methods have been introduced to evaluate probabilistic forecasts,…
This paper investigates how two important sources of risk -- market tail risk and extreme market volatility risk -- are priced into the cross-section of asset returns across various investment horizons. To identify such risks, we propose a…
In this paper we introduce and study several multivariate, heavy-tailed distribution classes, and we explore their closure properties and their applications. We consider the class of multivariate, positively decreasing distributions, and…