This paper investigates the coherent risk measure of normal mixture distributions. The main result shows that the mean-risk …-case value at risk in the robust portfolio optimization can also be calculated directly. Finally the conditional value at risk is … considered as an example of coherent risk measure; and we obtain the marginal contribution to risk for a portfolio based on …

distributions by deriving the closed-form expressions for the Conditional Value at Risk, a risk measure that is closely related to …

. We consider two risk measures, Value-at-Risk and Conditional-Value-at-Risk, and two types of decision makers, risk … neutral and risk averse. For Value-at-Risk, we show that the optimal solution does not change with the type of decision maker …. However, this observation is not true for Conditional-Value-at-Risk. We then show for Conditional-Value-at-Risk that the …

Extreme losses are the major concern in risk management. However, the dependence between financial assets and the … tail risk, the tail regression beta, defined by an asset's sensitivity to large negative market shocks, and establish the … the tail regression beta of industry portfolios to regular systematic risk measures: the market beta and the downside beta …

the present paper we call such combinations ‘coupled risk measures' and develop a statistical inferential theory for them …Considerable literature has been devoted to developing statistical inferential results for risk measures, especially … a number of risk measures that are of the form of ratios, or even more complex combinations, of two L-functionals. In …

market risk when the market experiences a substantial decline. This is also true when we consider a number of distinct hedge … fund styles. This source of risk is not diversifiable, and for this reason funds-of-funds as portfolios of hedge funds … concentrate tail risk exposure rather than mitigate this effect …

This paper investigates estimation of extreme risk in a number of stock markets in the Gulf Cooperation Council (GCC …