A characterization of multivariate regular variation

By Bojan Basrak, Richard A. Davis, Thomas Mikosch. 2002

192 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/426cd5473e6b21aa2614bd2039f18383311e73e3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

In Mathematical Physics

Citations in the corpus

The Extremal Dependence Measure and Asymptotic Independence (2004, background): “(2) When marginals are the same and b t = t or bn = n we are in the standard case 21,46 and all marginal distributions are tail equivalent to a standard Pareto distribution with = 1.”
Regular variation of GARCH processes (2002, background): “In Basrak et al. (2000) it was shown that the two de2nitions (2.5) and (2.6) are essentially equivalent, The motivation for studying this equivalence was the fact that Kesten’s theorem given below for solutions to stochastic recurrence equations states regular variation in the sense of (2.6), not…”
Asymptotic Results for the Sum of Dependent Non-identically Distributed Random Variables (2009, unknown): “[8].”
Properties and estimation of GARCH(1,1) model (2005, background): “random variables such that EZt = 0; (2) Z(2) t is nondegenerate; (3) for someδ > 0 existsSδ <∞ such thatE [ Z t ] ≤ Sδ <∞; (4) E [”
On the foundations of multivariate heavy-tail analysis (2004, background): “A different treatment of the polar coordinate transformation is given in [1], [2], [35].”
Decompositions of dependence for high-dimensional extremes (2016, background): “Berman et al. (2015) provides an overview of current knowledge and the status of several open problems concerning completely positive matrices.”
Regularly varying functions (2006, background): “[1], the last statements are due to Hult and Lindskog [26].”
Tail Risk of Multivariate Regular Variation (2011, background): “of MRV distributions can be found in [24, 25, 2 , 3].”
Fat tails, VaR and subadditivity☆ (2013, unknown): “5 For an encyclopedic treatment of regular variation, see Bingham et al. (1987) or Resnick (1987).”
Regularly varying multivariate time series (2007, background): “The following version for multivariate regular variation appears as Proposition A.1 in Basrak et al. (2002b).”
ON TAIL INDEX ESTIMATION FOR DEPENDENT, HETEROGENEOUS DATA (2010, background): “…2t = ω+ p ∑ i=1 βi X 2 t−i + q ∑ i=1 γiσ 2 t−i , α0 > 0, at least one βi ,γi > 0; the roots of 1− q ∑ i=1 γi z i lie outside unit circle; and the Lyapunov exponent γ < 0.3 Class (10) has regularly varying tails of the form P(|Xt | > x) = cx−κ(1 + o(1)), c > 0, α > 0 (Basrak et al., 2002, Thm. 3.1).”
Limit Laws for Random Vectors with an Extreme Component (2005, unknown): “From (25), we see that the distribution of (X∗, Y ) is standard regularly varying with limit measure μ∗ (see [3, 32, 37]) on the cone [0,∞] × (0,∞] and, therefore μ∗ is homogeneous of order -1: μ∗(c ) = c−1μ∗( ) ∀c > 0, where is a Borel subset of [0,∞] × (0,∞].”
Tail Dependence for Heavy-Tailed Scale Mixtures of Multivariate Distributions (2009, background): “1), which belong to the family of multivariate regularly varying distributions [1], [2].”
Tail asymptotics for the sum of two heavy-tailed dependent risks (2006, background): “2 Since the copula of a bivariate distribution stays invariant under strictly increasing transformations of the marginals and the tail dependence coefficient is a function of the copula only, Lemma 3.4 can be carried over to the random vector (X1, X2) = (eY1 , eY2) with lognormal marginals.”
Extremal behavior of regularly varying stochastic processes (2005, unknown): “variation for R-valued random vectors [1,2,14,16].”