The Gradient Allocation Principle based on the Higher Moment Risk Measure

According to the gradient allocation principle based on a positively homogeneous and subadditive risk measure, the capital allocated to a sub-portfolio is the Gâteaux derivative of the underlying risk measure at the overall portfolio in the direction of the sub-portfolio. We consider the gradient allocation principle based on the higher moment risk measure. In doing so we prove that this risk measure is Gâteaux differentiable and derive an explicit expression for the Gâteaux derivative. Then we prove that the plug-in estimator for the gradient allocation principle is strongly consistent and asymptotically normal. Finally, we consider some numerical studies.