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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…
In this paper, we consider the problem of computing estimates of the domain-of-attraction for non-polynomial systems. A polynomial approximation technique, based on multivariate polynomial interpolation and error analysis for remaining…
In this paper, according to a certain criterion, we divide the exponential distribution class into three subclasses. One of them is closely related to the regular-variation-tailed distribution class, so it is called the…
Many widely studied graphical models with latent variables lead to nontrivial constraints on the distribution of the observed variables. Inspired by the Bell inequalities in quantum mechanics, we refer to any linear inequality whose…
Latent traversal is a popular approach to visualize the disentangled latent representations. Given a bunch of variations in a single unit of the latent representation, it is expected that there is a change in a single factor of variation of…
We consider random matrix ensembles on the set of Hermitian matrices that are heavy tailed, in particular not all moments exist, and that are invariant under the conjugate action of the unitary group. The latter property entails that the…
Underpinning the success of deep learning is effective regularizations that allow a variety of priors in data to be modeled. For example, robustness to adversarial perturbations, and correlations between multiple modalities. However, most…
Model uncertainty has been one prominent issue both in the theory of risk measures and in practice such as financial risk management and regulation. Motivated by this observation, in this paper, we take a new perspective to describe the…
Convolutional neural networks (CNNs) have demonstrated gratifying results at learning discriminative features. However, when applied to unseen domains, state-of-the-art models are usually prone to errors due to domain shift. After…
Domain shifts in the training data are common in practical applications of machine learning; they occur for instance when the data is coming from different sources. Ideally, a ML model should work well independently of these shifts, for…
Multiple linear regression is a basic statistical tool, yielding a prediction formula with the input variables, slopes, and an intercept. But is it really easy to see which terms have the largest effect, or to explain why the prediction of…
Multi-domain translation seeks to learn a probabilistic coupling between marginal distributions that reflects the correspondence between different domains. We assume that data from different domains are generated from a shared latent…
In the mixture models problem it is assumed that there are $K$ distributions $\theta_{1},\ldots,\theta_{K}$ and one gets to observe a sample from a mixture of these distributions with unknown coefficients. The goal is to associate instances…
The aim of this paper is to present a mixture composite regression model for claim severity modelling. Claim severity modelling poses several challenges such as multimodality, heavy-tailedness and systematic effects in data. We tackle this…
In univariate data, there exist standard procedures for identifying dominating features that produce the largest observations. However, in the multivariate setting, the situation is quite different. This paper aims to provide tools and…
We propose a novel approach for domain generalisation (DG) leveraging risk distributions to characterise domains, thereby achieving domain invariance. In our findings, risk distributions effectively highlight differences between training…
We study explained variation under the additive hazards regression model for right-censored data. We consider different approaches for developing such a measure, and focus on one that estimates the proportion of variation in the failure…
Marginal expected shortfall is unquestionably one of the most popular systemic risk measures. Studying its extreme behaviour is particularly relevant for risk protection against severe global financial market downturns. In this context,…
We introduce a new family of multivariate distributions by taking the component-wise Tukey-h transformation of a random vector following a skew-normal distribution. The proposed distribution is named the skew-normal-Tukey-h distribution and…
We extend the class of tempered stable distributions first introduced in Rosinski 2007. Our new class allows for more structure and more variety of tail behaviors. We discuss various subclasses and the relation between them. To characterize…