基于概率半测度的风险度量
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摘要
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 financial 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 satisfies the convexity but also satisfies tonicity. Considering the importance of convexity and tonicity in portfolio selection and risk management, the proposed risk measure has certain theoretical value and practical significance.
In the financial 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 satisfies the convexity but also satisfies tonicity. Considering the importance of convexity and tonicity in portfolio selection and risk management, the proposed risk measure has certain theoretical value and practical significance.
引文
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[11]文平,马雪雅.基于Minkowski测度的风险度量[J].系统管理学报,2008,17(2):177-180Wen P,Ma X Y.The risk measure based on Minkowski gauge[J].Journal of Systems and Management,2008,17(2):177-180
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[13]Cillo A,Delqui′e P.Mean-risk analysis with enhanced behavioral content[J].European Journal of Operational Research,2014,239(3):764-775
[14]文平,秦伶俐.基于凸函数的风险测度[J].数学的实践与认识,2013,43(4):215-220Wen P,Qin L L.The risk measure based on convex function[J].Mathematics in Practice and Theory,2013,43(4):215-220
[15]Yamazaki S.Stochastic dominance,mean variance and Gini mean difference[J].The American Economic Review,1983,72(2):178-185
[16]Abeler J,Falk A,Goette L,et al.Reference points and effort provision[J].The American Economic Review,2011,101(2):470-492
[17]Marzilli Ericson K M,Fuster A.Expectations as endowments:evidence on reference-dependent preferences from exchange and valuation experiments[J].The Quarterly Journal of Economics,2011,126(4):1879-1907
[2]Konno H,Shirakawa H,Yamazaki H.A mean-absolute deviation-skewness portfolio optimization model[J].Annals of Operations Research,1993,45(2):205-220
[3]Roy A D.Safety first and the holding of assets[J].Econometrica,1952,20(3):431-449
[4]Bawa V S.Optimal rules for ordering uncertain prospects[J].Journal of Financial Economics,1975,2(1):95-121
[5]Fishburn P C.Mean-risk analysis with risk associated with below-target returns[J].American Economic Review,1977,67(2):116-126
[6]Artzner P,Delbaen F,Eber J,et al.Coherent measures of risk[J].Mathematical Finance,1999,35(3):203-228
[7]Rockafellar R T,Uryasev S.Conditional value-at-risk for general loss distributions[J].Journal of Banking and Finance,2002,26(7):1443-1471
[8]Tasche D.Expected shortfall and beyond[J].Journal of Banking and Finance,2002,26(7):1519-1533
[9]Pflug G C.How to Measure Risk?[C]//Leopold-Wildburger U,Feichtinger G,Kistner K P,Editor.Modelling and Decisions in Economics:Essays in Honor of Franz Ferschl,Berlin:Physica-Verlag,1999:39-59
[10]Giorgi E D.Reward-risk portfolio selection and stochastic dominance[J].Journal of Banking and Finance,2005,29(4):895-926
[11]文平,马雪雅.基于Minkowski测度的风险度量[J].系统管理学报,2008,17(2):177-180Wen P,Ma X Y.The risk measure based on Minkowski gauge[J].Journal of Systems and Management,2008,17(2):177-180
[12]K¨oszegi B,Rabin M.Reference-dependent risk attitudes[J].American Economic Review,2007,97(4):1047-1073
[13]Cillo A,Delqui′e P.Mean-risk analysis with enhanced behavioral content[J].European Journal of Operational Research,2014,239(3):764-775
[14]文平,秦伶俐.基于凸函数的风险测度[J].数学的实践与认识,2013,43(4):215-220Wen P,Qin L L.The risk measure based on convex function[J].Mathematics in Practice and Theory,2013,43(4):215-220
[15]Yamazaki S.Stochastic dominance,mean variance and Gini mean difference[J].The American Economic Review,1983,72(2):178-185
[16]Abeler J,Falk A,Goette L,et al.Reference points and effort provision[J].The American Economic Review,2011,101(2):470-492
[17]Marzilli Ericson K M,Fuster A.Expectations as endowments:evidence on reference-dependent preferences from exchange and valuation experiments[J].The Quarterly Journal of Economics,2011,126(4):1879-1907