一类特殊投资群体的谱风险度量及最优投资组合
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摘要
随着全球经济发展的一体化,金融市场的风险已经成为影响全球经济发展的重要因素。如何合理的度量投资者所面临的风险,已经成为现代金融理论的一个重要研究内容。风险度量的一种重要用处就是以不同的风险度量为目标函数进行投资组合的优化。
本文主要研究了一类特殊投资群体的谱风险度量,以及这类特殊投资群体的最优投资组合问题。这类特殊投资群体对待风险的厌恶程度不是一成不变或者单调的,而是一开始随着财富的增加,投资者的绝对风险厌恶程度是逐渐减小的,当财富超过一定的预期值后,随着财富的增加,投资者的绝对风险厌恶程度是逐渐增大的。本文首先分析风险在经济活动中的含义以及各种类型,其次介绍了各种风险度量风险方法,并且比较了优缺点,然后在不同的风险度量方法的基础上阐述了与之相对应的各种投资组合优化模型。最后利用谱风险度量,来构造这类特殊投资群体的谱风险度量函数,同时建立了以谱风险度量为目标函数的最优投资组合模型,并且选取上证股票市场的实际数据进行实证分析。
With the integration of global economic development, financial market risks have also become an important factor in global economic development. How to measure the risks faced by investors, has been to is an important research content in modern financial theory. risk measure is always used to to optimize the investment portfolio.
In this paper, we mainly study a special class of investment groups, the spectral risk measure. Investment groups' risk aversion is not monotonous, but beginning with the increasing of wealth, investors' absolute risk aversion is gradually reduced. When the wealth beyond a certain expected value, the investors' absolute risk aversion is gradually increasing. In this paper, firstly, we study the meaning of risk in economic, Second, we introduce a variety of risk measurement methods And compare their advantages and disadvantages and construct different portfolio optimization model. Finally we construct the spectral risk measure function with the method of SMR. At the same time,we establish a spectral risk measure as the objective function of the optimal portfolio model, and select the Shanghai stock market's actual data to vertify the theory.
本文主要研究了一类特殊投资群体的谱风险度量,以及这类特殊投资群体的最优投资组合问题。这类特殊投资群体对待风险的厌恶程度不是一成不变或者单调的,而是一开始随着财富的增加,投资者的绝对风险厌恶程度是逐渐减小的,当财富超过一定的预期值后,随着财富的增加,投资者的绝对风险厌恶程度是逐渐增大的。本文首先分析风险在经济活动中的含义以及各种类型,其次介绍了各种风险度量风险方法,并且比较了优缺点,然后在不同的风险度量方法的基础上阐述了与之相对应的各种投资组合优化模型。最后利用谱风险度量,来构造这类特殊投资群体的谱风险度量函数,同时建立了以谱风险度量为目标函数的最优投资组合模型,并且选取上证股票市场的实际数据进行实证分析。
With the integration of global economic development, financial market risks have also become an important factor in global economic development. How to measure the risks faced by investors, has been to is an important research content in modern financial theory. risk measure is always used to to optimize the investment portfolio.
In this paper, we mainly study a special class of investment groups, the spectral risk measure. Investment groups' risk aversion is not monotonous, but beginning with the increasing of wealth, investors' absolute risk aversion is gradually reduced. When the wealth beyond a certain expected value, the investors' absolute risk aversion is gradually increasing. In this paper, firstly, we study the meaning of risk in economic, Second, we introduce a variety of risk measurement methods And compare their advantages and disadvantages and construct different portfolio optimization model. Finally we construct the spectral risk measure function with the method of SMR. At the same time,we establish a spectral risk measure as the objective function of the optimal portfolio model, and select the Shanghai stock market's actual data to vertify the theory.
引文
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[3]Cormac Butler.《风险值概论》.[M].上海财经大学出版社.
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[6]李国敏.《基于谱风险测度风险计量指标的银行投资组合模型》.[M].统计与决策.2007,(1).
[7]莫顿.《连续时间金融》.[M].机械工业出版社.
[8]伯恩斯坦.《资本理想》.[M].机械工业出版社.
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[10]《金融工程师系统》.www. fingineer. com.
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[12]李国敏.《基于谱风险测度风险计量指标的银行投资组合模型》.[M].统计与决策.2007,(1).
[13]刘俊山《基于风险测度理论的证券投资组合优化研究》.[J].2007.4
[14]薛嘉庆.《线性规划》.[M].高等教育出版社
[15]朱世武.《金融计算与建模》.[M].清华大学出版社
[16]宋逢明.《金融经济学导论》.[M].高等教育出版社
[17]薛定宇.《高等应用数学问题的MATLAB求解》.[M].清华大学出版社
[18]史树中.《金融经济学十讲》.[M].上海人民出版社
[19]郭多祚.《数理金融》.[M].清华大学出版社
[20]罗伯特.《微观经济学》.[M].中国人民大学出版社
[21]邵宇.《微观金融学及其数学基础》.[M].清华大学出版社
[22]Cox,Huang(1989). 《Bhattcharya》.[M].p283.
[23]Alexander C.Market Models. A Guide to Financial Data Analysis[M].
[24]Acerbi C. Spectral measures of risk:A coherent representation of subjective rik aversion[J]. Journal of Banking and Finance,2002,26, (7)
[25]Jorion P.Value at Risk:The New Benchmark for Managing Financial Risk[M].2nd edition,2001
[26]Dowd K. An Introduction to Market Risk Measurement [M]. Chicheser:Wiley Press,2002
[27]Hull J. Options, Futures and Other Derivatives [M] 6th edition,2006
[28]Tsay R. Analysis of Financial Time Series [M].Chichester:Wiley Press,2nd editon,2005
[29]Artzner P, Delbaen F, Eber J M, et al. Coherent measures of risk[J].Mathematical Finance,1999
[30]Adam A, Houkari M, Laurent J P. Spectral Risk measures and portfolio selection[J]. Journal of Banking and Finance,2008
[31]KendallM G. Anew measure of rank correlation [J]. Biometrika,1987
[32]Morgan J P. RiskMetrics, Technology Document 4th Edition[M].New York Riskmetrics Group,1996
[33]Dowd K. Measuring Market Risk[M].New York John Wiley& Sons Ltd,2002
[34]Nelsen T A, etal Black smokers, massive sulf ides and vent biota at the Mid-Atlantic Ridge[J].Nature,1986
[35]Nelsen R B.An introduction to Copulas[M].New York Springer,1999
[36]Genest C.Frank's family of bivariate distributions [J].Biametrika,1987
[37]Genset C, Rivest L P. Statistical inference copulas[J]. J. Amer. Statist. Assoc,1999.
[38]Ceske R, Hernandez JV, Sanchez LM. Quantifying event risk:the next convergence[J]. The Journal of Risk Finance,2000
[39]Bouye E. Copulas for Finance, A Reaging Guide and Some Applications[M]. london
[40]Campbell, John. Asset Pricing at the Millennium[J]The Journal of Finance,2000,4
[2]王明涛.《金融风险计量与管理》.[M].上海财经大学出版社.
[3]Cormac Butler.《风险值概论》.[M].上海财经大学出版社.
[4]菲利普·乔瑞.《风险价值VaR》.[M].中信出版社.
[5]王春峰.《金融市场风险管理》.[M].天津大学出版社.
[6]李国敏.《基于谱风险测度风险计量指标的银行投资组合模型》.[M].统计与决策.2007,(1).
[7]莫顿.《连续时间金融》.[M].机械工业出版社.
[8]伯恩斯坦.《资本理想》.[M].机械工业出版社.
[9]伯恩斯坦.《风险值概论》.[M].上海财经大学出版社.
[10]《金融工程师系统》.www. fingineer. com.
[11]勒威.《证券投资组合与选择》.[M].中山大学出版社
[12]李国敏.《基于谱风险测度风险计量指标的银行投资组合模型》.[M].统计与决策.2007,(1).
[13]刘俊山《基于风险测度理论的证券投资组合优化研究》.[J].2007.4
[14]薛嘉庆.《线性规划》.[M].高等教育出版社
[15]朱世武.《金融计算与建模》.[M].清华大学出版社
[16]宋逢明.《金融经济学导论》.[M].高等教育出版社
[17]薛定宇.《高等应用数学问题的MATLAB求解》.[M].清华大学出版社
[18]史树中.《金融经济学十讲》.[M].上海人民出版社
[19]郭多祚.《数理金融》.[M].清华大学出版社
[20]罗伯特.《微观经济学》.[M].中国人民大学出版社
[21]邵宇.《微观金融学及其数学基础》.[M].清华大学出版社
[22]Cox,Huang(1989). 《Bhattcharya》.[M].p283.
[23]Alexander C.Market Models. A Guide to Financial Data Analysis[M].
[24]Acerbi C. Spectral measures of risk:A coherent representation of subjective rik aversion[J]. Journal of Banking and Finance,2002,26, (7)
[25]Jorion P.Value at Risk:The New Benchmark for Managing Financial Risk[M].2nd edition,2001
[26]Dowd K. An Introduction to Market Risk Measurement [M]. Chicheser:Wiley Press,2002
[27]Hull J. Options, Futures and Other Derivatives [M] 6th edition,2006
[28]Tsay R. Analysis of Financial Time Series [M].Chichester:Wiley Press,2nd editon,2005
[29]Artzner P, Delbaen F, Eber J M, et al. Coherent measures of risk[J].Mathematical Finance,1999
[30]Adam A, Houkari M, Laurent J P. Spectral Risk measures and portfolio selection[J]. Journal of Banking and Finance,2008
[31]KendallM G. Anew measure of rank correlation [J]. Biometrika,1987
[32]Morgan J P. RiskMetrics, Technology Document 4th Edition[M].New York Riskmetrics Group,1996
[33]Dowd K. Measuring Market Risk[M].New York John Wiley& Sons Ltd,2002
[34]Nelsen T A, etal Black smokers, massive sulf ides and vent biota at the Mid-Atlantic Ridge[J].Nature,1986
[35]Nelsen R B.An introduction to Copulas[M].New York Springer,1999
[36]Genest C.Frank's family of bivariate distributions [J].Biametrika,1987
[37]Genset C, Rivest L P. Statistical inference copulas[J]. J. Amer. Statist. Assoc,1999.
[38]Ceske R, Hernandez JV, Sanchez LM. Quantifying event risk:the next convergence[J]. The Journal of Risk Finance,2000
[39]Bouye E. Copulas for Finance, A Reaging Guide and Some Applications[M]. london
[40]Campbell, John. Asset Pricing at the Millennium[J]The Journal of Finance,2000,4