Risk management under Omega measure

We prove that the Omega measure, which considers all moments when assessing portfolio performance, is equivalent to the widely used Sharpe ratio under jointly elliptic distributions of returns. Portfolio optimization of the Sharpe ratio is then explored, with an active-set algorithm presented for markets prohibiting short sales. When asymmetric returns are considered we show that the Omega measure and Sharpe ratio lead to different optimal portfolios

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 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

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 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.

Risk aggregation in Solvency II: How to converge the approaches of the internal models and those of the standard formula?

Two approaches may be considered in order to determine the Solvency II economic capital: the use of a standard formula or the use of an internal model (global or partial). However, the results produced by these two methods are rarely similar, since the underlying hypothesis of marginal capital aggregation is not verified by the projection models used by companies. We demonstrate that the standard formula can be considered as a first order approximation of the result of the internal model. We therefore propose an alternative method of aggregation that enables to satisfactorily capture the diversity among the various risks that are considered, and to converge the internal models and the standard formula.