Performance ratio-based coherent risk measure and its application
提出一种名为广义短缺风险度量的一般方法，用于构建一致风险度量，并重点研究其子类——基于绩效比率的一致风险度量，该度量易于处理且具有金融解释，在考虑交易成本的投资组合选择模型中表现优于高阶矩一致风险度量。
Utilizing a specific acceptance set, we propose in this paper a general method to construct coherent risk measures called the generalized shortfall risk measure. Besides some existing coherent risk measures, several new types of coherent risk measures can be generated. We investigate the generalized shortfall risk measure’s desirable properties such as consistency with second-order stochastic dominance. By combining the performance evaluation with the risk control, we study in particular the performance ratio-based coherent risk (PRCR) measures, which is a sub-class of generalized shortfall risk measures. The PRCR measures are tractable and have a suitable financial interpretation. Based on the PRCR measure, we establish a portfolio selection model with transaction costs. Empirical results show that the optimal portfolio obtained under the PRCR measure performs much better than the corresponding optimal portfolio obtained under the higher moment coherent risk measure.