基于概率半测度的风险度量

Risk Measures Based on Probability Semimetric

在金融风险管理中,对风险度量方法的研究一直是该领域的一项重要内容.我们先利用概率测度以及凸函数构造了一种风险度量,但是发现该度量不满足协调性以及下侧风险的思想.我们又利用凸函数构造了基于半概率测度的风险度量,发现该风险度量方法包括了许多常见的风险度量方法,如半方差、半绝对离差、下偏矩、ES等.研究表明新风险度量不仅满足凸性而且还满足协调性.考虑到凸性以及协调性在投资组合以及风险管理中的重要意义,该风险度量方法具有一定的研究价值和实际意义.

In the fnancial risk management, research on the method of risk measures has always been an important topic. We use probability metric and convex function to construct a new risk measure. Since the risk measure does not satisfy tonicity and the idea of downside risk, we use convex function to construct new risk measures based on the probability semi-metric. It is found that the new risk measurement method includes many common risk measures, for example, semi-variance, semi-absolute deviation, the lower partial moment and ES. We show that the risk measure not only satisfes the convexity but also satisfes tonicity. Considering the importance of convexity and tonicity in portfolio selection and risk management, the proposed risk measure has certain theoretical value and practical signifcance.