Abstract
This paper investigates the coherent risk measure of normal mixture distributions. The main result shows that the mean-risk portfolio optimization problem of some widely-used normal mixture distributions can be reduced to a quadratic programming problem which has closed form of solution by fixing the location parameter and skewness parameter. In addition, the worst-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 normal mixture model.
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