Related papers: A Peer-based Model of Fat-tailed Outcomes
We study the asymptotic behaviour of widely used tests for evaluating and comparing predictive accuracy when forecast errors exhibit heavy tails. In particular, when loss differentials have infinite variance, the Diebold-Mariano test…
This paper introduces the multivariate tail-inflated normal (MTIN) distribution, an elliptical heavy-tails generalization of the multivariate normal (MN). The MTIN belongs to the family of MN scale mixtures by choosing a convenient…
In the standard equilibrium and/or arbitrage pricing framework, the value of any asset is uniquely specified from the belief that only the systematic risks need to be remunerated by the market. Here, we show that, even for arbitrary large…
For purposes of Value-at-Risk estimation, we consider several multivariate families of heavy-tailed distributions, which can be seen as multidimensional versions of Paretian stable and Student's t distributions allowing different marginals…
We derive the sharp non-asymptotical uniform estimations for tails of distributions for classical normed sums of centered normed independent random vectors having a moderate decreasing individual tails of summands.
Understanding the shape of a distribution of data is of interest to people in a great variety of fields, as it may affect the types of algorithms used for that data. We study one such problem in the framework of distribution property…
Insurance data can be asymmetric with heavy tails, causing inadequate adjustments of the usually applied models. To deal with this issue, hierarchical models for collective risk with heavy-tails of the claims distributions that take also…
Recently some papers, such as Aban, Meerschaert and Panorska (2006), Nuyts (2010) and Clark (2013), have drawn attention to possible truncation in Pareto tail modelling. Sometimes natural upper bounds exist that truncate the probability…
Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the…
We develop an econometric framework integrating heavy-tailed Student's $t$ distributions with behavioral probability weighting while preserving infinite divisibility. Using 432{,}752 observations across 86 assets (2004--2024), we…
Given an arbitrary continuous probability density function, it is introduced a conjugated probability density, which is defined through the Shannon information associated with its cumulative distribution function. These new densities are…
Let F be a distribution function with negative mean and regularly varying right tail. Under a mild smoothness condition we derive higher order asymptotic expansions for the tail distribution of the maxima of the random walk generated by F.…
Standard, PCA-based factor analysis suffers from a number of well known problems due to the random nature of pairwise correlations of asset returns. We analyse an alternative based on ICA, where factors are identified based on their…
We propose a simple data model inspired from natural data such as text or images, and use it to study the importance of learning features in order to achieve good generalization. Our data model follows a long-tailed distribution in the…
Returns distributions are heavy-tailed across asset classes. In this note, I examine the implications of this well-known stylized fact for the joint statistics of performance (absolute return) and Sharpe ratio (risk-adjusted return). Using…
This paper introduces a new distribution to improve tail risk modeling. Based on the classical normal distribution, we define a new distribution by a series of heat equations. Then, we use market data to verify our model.
Considerable literature has been devoted to developing statistical inferential results for risk measures, especially for those that are of the form of L-functionals. However, practical and theoretical considerations have highlighted quite a…
We construct an example of a continuous centered random process with light tails of finite-dimensional distribution but with heavy tail of maximum distribution.
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,…
Power-law tail behavior and the summation scheme of Levy-stable distributions is the basis for their frequent use as models when fat tails above a Gaussian distribution are observed. However, recent studies suggest that financial asset…