Value-at-Risk and Expected Shortfall for Linear Portfolios with elliptically distributed RisK Factors

In this paper, we generalize the parametric Delta-VaR method from portfolios with normally distributed risk factors to portfolios with elliptically distributed ones. We treat both expected shortfall and the Value-at-Risk of such portfolios. Special attention is given to the particular case of a multivariate t-distribution.Delta Elliptic VaR, Delta Elliptic ES, Delta Student VaR, Delta Student ES

VaR and ES for linear Portfolis with mixture of elliptically distributed Risk Factors.

The particular subject of this paper, is to give an explicit formulas that will permit to obtain the linear VaR or Linear ES, when the joint risk factors of the Linear portfolios, changes with mixture of t-Student distributions. Note that, since one shortcoming of the multivariate t- distribution is that all the marginal distributions must have the same degrees of freedom, which implies that all risk factors have equally heavy tails, the mixture of t-Student will be view as a serious alternatives, to a simple t-Student-distribution. Therefore, the methodology proposes by this paper seem to be interesting to controlled thicker tails than the standard Student distribution.sadefo-kamdem

Coefficient of variation and Power Pen's parade computation

Under the the assumption that income y is a power function of its rank among n individuals, we approximate the coefficient of variation and gini index as functions of the power degree of the Pen's parade. Reciprocally, for a given coefficient of variation or gini index, we propose the analytic expression of the degree of the power Pen's parade; we can then compute the Pen's parade.Gini index, Income inequality, Ranks, Har- monic Number, Pen's Parade.

INTEGRAL TRANSFORMS WITH THE HOMOTOPY PERTURBATION METHOD AND SOME APPLICATIONS

This paper applies He's homotopy perturbation method to compute a large variety of integral transforms. As illustration, the paper gives special attention to the Esscher transform, the Fourier transform, the Hankel transform, the Mellin transform, the Stieljes transform and some applications.He's homotopy method; integral transforms; linear equations; Type G and spherical distributions, Random variable.

VaR and ES for Linear Portfolios with mixture of Generalized Laplace Distributed Risk Factors

RiskMetrics Delta-Normal VaR, Delta-GLD-VaR, Delta-MGLD, Delta-GLD ES, Delta-MGLD, Hedge Funds Risk.

Gini Index and Polynomial Pen's Parade

In this paper, we propose a simple way to compute the Gini index when income y is a finite order k polynomial function of its rank among n individuals.Gini, Income inequality, Polynomial pen's parade, Ranks.

VaR and ES for linear Portfolios with mixture of elliptically distributed Risk Factors.

The particular subject of this paper, is to give an explicit formulas that will permit to obtain the linear VaR or Linear ES, when the joint risk factors of the Linear portfolios, changes with mixture of t-Student distributions. Note that, since one shortcoming of the multivariate t- distribution is that all the marginal distributions must have the same degrees of freedom, which implies that all risk factors have equally heavy tails, the mixture of t-Student will be view as a serious alternatives, to a simple t-Student-distribution. Therefore, the methodology proposes by this paper seem to be interesting to controlled thicker tails than the standard Student distribution.Delta mixture Elliptic VaR, Delta mixture Student VaR, Delta mixture Elliptic ES, Delta mixture Student ES, VaR Models.

VAR FOR QUADRATIC PORTFOLIO'S WITH GENERALIZED LAPLACE DISTRIBUTED RETURNS

This paper is concerned with the e±cient analytical computation of Value-at-Risk (VaR) for portfolios of assets depending quadratically on a large number of joint risk factors that follows a multivariate Generalized Laplace Distribution. Our approach is designed to supplement the usual Monte-Carlo techniques, by providing an asymptotic formula for the quadratic portfolio's cumulative distribution function, together with explicit error-estimates. The application of these methods is demonstrated using some financial applications examples.