5 research outputs found
Asymptotics of the Norm of Elliptical Random Vectors
In this paper we consider elliptical random vectors X in R^d,d>1 with
stochastic representation A R U where R is a positive random radius independent
of the random vector U which is uniformly distributed on the unit sphere of R^d
and A is a given matrix. The main result of this paper is an asymptotic
expansion of the tail probability of the norm of X derived under the assumption
that R has distribution function is in the Gumbel or the Weibull max-domain of
attraction.Comment: 11 page
Extremes of Aggregated Dirichlet Risks
The class of Dirichlet random vectors is central in numerous probabilistic
and statistical applications. The main result of this paper derives the exact
tail asymptotics of the aggregated risk of powers of Dirichlet random vectors
when the radial component has df in the Gumbel or the Weibull max-domain of
attraction. We present further results for the joint asymptotic independence
and the max-sum equivalence.Comment: published versio
Asymptotics of Random Contractions
In this paper we discuss the asymptotic behaviour of random contractions
, where , with distribution function , is a positive random
variable independent of . Random contractions appear naturally in
insurance and finance. Our principal contribution is the derivation of the tail
asymptotics of assuming that is in the max-domain of attraction of an
extreme value distribution and the distribution function of satisfies a
regular variation property. We apply our result to derive the asymptotics of
the probability of ruin for a particular discrete-time risk model. Further we
quantify in our asymptotic setting the effect of the random scaling on the
Conditional Tail Expectations, risk aggregation, and derive the joint
asymptotic distribution of linear combinations of random contractions.Comment: 25 page
Asymptotic expansion of Gaussian chaos via probabilistic approach
For a centered d-dimensional Gaussian random vector xi = (xi(1),..., xi (d) ) and a homogeneous function h : R-d -> R we derive asymptotic expansions for the tail of the Gaussian chaos h(xi) given the function h is sufficiently smooth. Three challenging instances of the Gaussian chaos are the determinant of a Gaussian matrix, the Gaussian orthogonal ensemble and the diameter of random Gaussian clouds. Using a direct probabilistic asymptotic method, we investigate both the asymptotic behaviour of the tail distribution of h(xi) and its density at infinity and then discuss possible extensions for some general xi with polar representation
Asymptotics of the norm of elliptical random vectors
In this paper we consider elliptical random vectors in with stochastic representation , where R is a positive random radius independent of the random vector which is uniformly distributed on the unit sphere of and is a given matrix. Denote by ||[dot operator]|| the Euclidean norm in , and let F be the distribution function of R. The main result of this paper is an asymptotic expansion of the probability for F in the Gumbel or the Weibull max-domain of attraction. In the special case that is a mean zero Gaussian random vector our result coincides with the one derived in Hüsler et al. (2002) [1].Elliptical distribution Gaussian distribution Kotz Type distribution Gumbel max-domain of attraction Tail approximation Density convergence Weak convergence