Related papers: A Breiman's theorem for conditional dependent rand…
We propose a random walk model of asset returns where the parameters depend on market stress. Stress is measured by, e.g., the value of an implied volatility index. We show that model parameters including standard deviations and…
In this paper we consider a telegraph equation with time-dependent coefficients, governing the persistent random walk of a particle moving on the line with a time-varying velocity $c(t)$ and changing direction at instants distributed…
Heavy tailed phenomena are naturally analyzed by extreme value statistics. A crucial step in such an analysis is the estimation of the extreme value index, which describes the tail heaviness of the underlying probability distribution. We…
A common object to describe the extremal dependence of a $d$-variate random vector $X$ is the stable tail dependence function $L$. Various parametric models have emerged, with a popular subclass consisting of those stable tail dependence…
Different models to study the wealth distribution in an artificial society have considered a transactional dynamics as the driving force. Those models include a risk aversion factor, but also a finite probability of favoring the poorer…
Estimation of the complete distribution of a random variable is a useful primitive for both manual and automated decision making. This problem has received extensive attention in the i.i.d. setting, but the arbitrary data dependent setting…
We estimate generic statistical properties of a structural credit risk model by considering an ensemble of correlation matrices. This ensemble is set up by Random Matrix Theory. We demonstrate analytically that the presence of correlations…
We establish the one-to one bilateral interrelations between an asymptotic behavior for the tail of distributions for random variables and its great moments evaluation. Our results generalize the famous Richter's ones.
We study the tail behavior of the distribution of the sum of asymptotically independent risks whose marginal distributions belong to the maximal domain of attraction of the Gumbel distribution. We impose conditions on the distribution of…
Multivariate regular variation plays a role assessing tail risk in diverse applications such as finance, telecommunications, insurance and environmental science. The classical theory, being based on an asymptotic model, sometimes leads to…
In this paper, we study a multidimensional risk model with a common renewal process and in the presence of a constant interest force. The claim sizes are independent and identically distributed random vectors, with the distribution of…
The possibilities of the use of the coefficient of variation over a high threshold in tail modelling are discussed. The paper also considers multiple threshold tests for a generalized Pareto distribution, together with a threshold selection…
We propose information criteria that measure the prediction risk of a predictive density based on the Bayesian marginal likelihood from a frequentist point of view. We derive criteria for selecting variables in linear regression models,…
The contribution of this paper is to introduce change of measure based techniques for the rare-event analysis of heavy-tailed stochastic processes. Our changes-of-measure are parameterized by a family of distributions admitting a mixture…
In the context of bounding probability of small deviation, there are limited general tools. However, such bounds have been widely applied in graph theory and inventory management. We introduce a common approach to substantially sharpen such…
Following Feynman's treatment of the non-relativistic polaron problem, similar techniques are used to study relativistic field theories: after integrating out the bosonic degrees of freedom the resulting effective action is formulated in…
In this paper, we study dependence uncertainty and the resulting effects on tail risk measures, which play a fundamental role in modern risk management. We introduce the notion of a regular dependence measure, defined on multi-marginal…
An insurance company is required to prepare a certain amount of money, called reserve, as a mean to pay its policy holders claims in the future. There are several types of reserve, one of them is IBNR reserve, for which the payments are…
The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…
Weighted empirical risk minimization is a common approach to prediction under distribution drift. This article studies its out-of-sample prediction error under nonstationarity. We provide a general decomposition of the excess risk into a…