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

On the residual dependence index of elliptical distributions

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 we calculate the partial residual dependence indices of a multivariate elliptical random vector assuming that the associated random radius is in the Gumbel max-domain of attraction. Furthermore, we discuss the estimation of these indices when the associated random radius possesses a Weibull-tail distribution.Comment: 11 pages, case \theta=1 now include

TAX SYSTEMS IN WEST BALKANS COUNTRIES – BETWEEN SIMPLICITY AND EFFICIENCY

There are two main features characterized every tax system: simplicity and efficiency. These features converge not necessarily with each other. The simplicity of a tax system is related and implies the simplicity of tax calculation. In other site this characteristic is a very important element regarding tax collection and also affects the transparency among different economics activities. But how much these system are efficient? The efficiency of a fiscal system is related particularly with the characteristic of a tax as an instrument for implementation of different economic policies, incitement of economic development, achievement of particular structural changes, etc. In this framework the paper aims to perform a comparative analyze of fiscal systems for different West Balkans Countries. The main objective of the paper is to analyze how much the tax systems of these countries reflect the simplicity and transparency, and in the other site, how much those serve as a mechanism of economic development. In this approach the paper effort to explain, if the tax systems are considerate only as an instrument of budget revenue collection, or these system have considerate also as an incentives targeted economic development of these countries.Tax System, simplicity, efficiency

Tail approximation for reinsurance portfolios of Gaussian-like risks

We consider two different portfolios of proportional reinsurance of the same pool of risks. This contribution is concerned with Gaussian-like risks, which means that for large values the survival function of such risks is, up to a multiplier, the same as that of a standard Gaussian risk. We establish the tail asymptotic behavior of the total loss of each of the reinsurance portfolios and determine also the relation between randomly scaled Gaussian-like portfolios and unscaled ones. Further we show that jointly two portfolios of Gaussian-like risks exhibit asymptotic independence and their weak tail dependence coefficient is non-negative.Comment: In press, Scandinavian Actuarial Journa

Conditional Limit Results for Type I Polar Distributions

Let (S_1,S_2)=(R \cos(\Theta), R \sin (\Theta)) be a bivariate random vector with associated random radius R which has distribution function $F$ being further independent of the random angle \Theta. In this paper we investigate the asymptotic behaviour of the conditional survivor probability \Psi_{\rho,u}(y):=\pk{\rho S_1+ \sqrt{1- \rho^2} S_2> y \lvert S_1> u}, \rho \in (-1,1),\in R when u approaches the upper endpoint of F. On the density function of \Theta we require a certain local asymptotic behaviour at 0, whereas for F we require that it belongs to the Gumbel max-domain of attraction. The main result of this contribution is an asymptotic expansion of \Psi_{\rho,u}, which is then utilised to construct two estimators for the conditional distribution function 1- \Psi_{\rho,u}. Further, we allow \Theta to depend on u.Comment: 14 pages, paper submitted to Extremes in 200