The residual dependence index of bivariate Gaussian distributions is determined by the correlation coefficient. This tail index is of certain statistical importance when extremes and related rare events of bivariate samples with asymptotic independent components are being modeled. In this paper...

Let X1,X2,... be independent bivariate claim sizes arising from an insurance portfolio. The number of claims occurring in the time interval [0,t] is denoted by N(t). We investigate in this paper distributional and asymptotic properties of the following point process:with XN(t):N(t), the...

Let {Xn, n[greater-or-equal, slanted]1} be a sequence of independent random variables with common continuous distribution function F and constants. In this short note an asymptotic evaluation of P{max1[less-than-or-equals, slant]i[less-than-or-equals, slant]n Xi[less-than-or-equals,...

Let S=(S1,...,Sd)[inverted perpendicular],d[greater-or-equal, slanted]2 be a spherical random vector in and let X=A[inverted perpendicular]S be an elliptical random vector with a non-singular matrix. Berman (1992. Sojourns and Extremes of Stochastic Processes. Wadsworth & Brooks/Cole) proved...

Let {Xi, i[greater-or-equal, slanted]1} be a sequence of independent random vectors with common continuous distribution function F. In this paper, we consider the number of the elements from X1,...,Xn which fall in some random region determined by the maximum. Both distributional and asymptotic...

In this paper we consider elliptical random vectors in with stochastic representation RAU where R is a positive random radius independent of the random vector U which is uniformly distributed on the unit sphere of and is a non-singular matrix. When R has distribution function in the Weibull...

Assuming that the claim sizes of an insurance company have a common distribution with gamma-like tail, we study the asymptotic tail behaviour of the reinsured amounts under the ECOMOR and LCR reinsurance treaties, respectively. Our novel results include a precise asymptotic expansion for the...

Random deflation of risk models is an interesting topic for both theoretical and practical actuarial problems. In this paper, we investigate second-order tail asymptotics of the deflated risk X=RS under the assumptions of second-order regular variation on the survival functions of the risk R and...