Related papers: Tail Asymptotics of Deflated Risks

Risk contagion concerns any entity dealing with large scale risks. Suppose (X,Y) denotes a risk vector pertaining to two components in some system. A relevant measurement of risk contagion would be to quantify the amount of influence of…

Tail Value-at-Risk (TVaR) is a widely adopted risk measure playing a critically important role in both academic research and industry practice in insurance. In data applications, TVaR is often estimated using the empirical method, owing to…

Using a family of modified Weibull distributions, encompassing both sub-exponentials and super-exponentials, to parameterize the marginal distributions of asset returns and their multivariate generalizations with Gaussian copulas, we offer…

We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the…

We study bivariate stochastic recurrence equations with triangular matrix coefficients and we characterize the tail behavior of their stationary solutions ${\bf W} =(W_1,W_2)$. Recently it has been observed that $W_1,W_2$ may exhibit…

We consider a two dimensional reflecting random walk on the nonnegative integer quadrant. This random walk is assumed to be skip free in the direction to the boundary of the quadrant, but may have unbounded jumps in the opposite direction,…

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…

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 risk management, tail risks are of crucial importance. The quality of a tail model, which is determined by data from an unknown distribution, depends critically on the subset of data used to model the tail. Based on a suitably weighted…

If the Euclidean norm is strongly concentrated with respect to a measure, the average distribution of an average marginal of this measure has Gaussian asymptotics that captures tail behaviour. If the marginals of the measure have…

Motivated by the empirical observation of power-law distributions in the credits (e.g., ``likes'') of viral posts in social media, we introduce a high-dimensional tail index regression model and propose methods for estimation and inference…

Stochastic volatility processes with heavy-tailed innovations are a well-known model for financial time series. In these models, the extremes of the log returns are mainly driven by the extremes of the i.i.d. innovation sequence which leads…

Let (RU_1, R U_2) be a given bivariate scale mixture random vector, with R>0 being independent of the bivariate random vector (U_1,U_2). In this paper we derive exact asymptotic expansions of the tail probability P{RU_1> x, RU_2> ax}, a \in…

Let $\{X(t)= (X_1(t),X_2(t))^T,\ t \in \mathbb{R}^N\}$ be an $\mathbb{R}^2$-valued continuous locally stationary Gaussian random field with $\mathbb{E}[X(t)]=\mathbf{0}$. For any compact sets $A_1, A_2 \subset \mathbb{R}^N$, precise…

This book chapter illustrates how to apply extreme value statistics to financial time series data. Such data often exhibits strong serial dependence, which complicates assessment of tail risks. We discuss the two main approches to tail risk…

Applying a modification of Extreme value Theory (thanks to a dual distribution technique by the authors on data over the past 2,500 years, we show that pandemics are extremely fat-tailed in terms of fatalities, with a marked potentially…

This research incorporates realized volatility and overnight information into risk models, wherein the overnight return often contributes significantly to the total return volatility. Extending a semi-parametric regression model based on…

This paper contributes to answering a question that is of crucial importance in risk management and extreme value theory: How to select the threshold above which one assumes that the tail of a distribution follows a generalized Pareto…

We study tails of the supremum of a perturbed random walk under regime which was not yet considered in the literature. Our approach is based on a new renewal theorem, which is of independent interest. We obtain first and second order…

We propose a variational tail bound for norms of random vectors under moment assumptions on their one-dimensional marginals. A simplified version of the bound that parametrizes the ``aggregating distribution'' using a certain pushforward of…