证券投资风险值VaR的度量与组合优化研究
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摘要
伴随着全球经济一体化、投资自由化以及金融创新的不断深入，金融市场的波动性和风险也在不断加剧，对于金融风险的管理已经成为金融机构和投资者所面临的最重要问题。VaR(Value at Risk)即风险值，作为金融风险分析、测度与防范的重要工具，是近年来国际上兴起的一种定量度量金融风险的管理方法。它是将众多不可测的主观因素转化为运用数理统计方法和计量技术的客观概率数值，使隐性风险显性化。VaR的概念虽简单，然而对它的度量却是一个具有挑战性的统计问题。
本文就金融风险管理研究的起源、金融风险的定义及分类、金融风险管理存在的理论基础以及现代金融风险管理的主流模型和方法技术做出了综述。在此基础上，重点研究了证券投资组合选择与组合评价的理论，并提出了金融风险管理研究未来可能的发展方向。主要研究有：
(1) 对目前国内外学术界对风险的定义进行了归纳和综述。归纳出七种学说观点，并对各种学说观点进行了评述和数量刻画。目前学术界对风险的内涵没有统一的定义，针对不同的风险源、风险管理的不同目标，不同的学者对风险的理解和认识程度与研究角度的不同，产生了不同的风险度量方法。通过对各种学说的归纳和总结，反映了人们对风险的认识不断深化、不断完善的递进过程。从现有的风险定义出发，重点分析了证券投资领域投资风险的特殊性，探讨了证券投资风险的本质特征。指出用VaR来描述金融市场风险将更为全面合理。
(2) 对中国股票市场收益率序列基本性质的研究。运用SAS和S-plus统计软件对上海股票市场收益率分布的正态性、自相关性、异方差性、独立同分布性等进行了相应的统计检验。实证分析与检验结果表明，在中国股票市场中，收益率序列具有明显的非正态特征，收益率序列独立同分布的假设被拒绝。收益率序列呈“尖峰厚尾”分布，且序列之间存在着明显的自相关性。
(3) 建立了风险值VaR的基本概念和理论分析框架。给出了服从几何布朗运动的股票和期权的VaR。紧密跟踪学科发展的前沿，对VaR度量的新方法进行了研究。针对模型中要求收益分布服从正态分布的假定，对VaR进行了拓展研究，引入了最坏条件VaR(worst-case VaR，WCVaR)的概念，并给出了它的计算公式。为了检验度量VaR方法的有效性，引入了Kupirc所给出的后验检验统计量，并采用似然比检验的方法，给出了模型有效的拒绝域。
(4) 首次提出了循环修正的组合评价方法。针对目前多指标综合评价方法很多，各种方法的出发点不同，解决问题的思路不同，适用的对象不同等，存在着
With the deepening of global economics integration, investment free port and financial innovation, the financial magnate's volatility and risk are also increased. The financial risk management has become the most important question which is the financial policy and the investor are facing. VaR, that is Value at Risk, as the main way to analyzing, measuring and preventing the financial risk. It is a kind of management way which has just come out to measure the financial risk in the world. It offered us a modern management theoretical conception and thinking. VaR is the method of converting many unmeasurable subjective factors into objective probability numeral value using mathematical statistic and measuring technology. This made the risk obvious and convenient to be managed and controlled. The conception of the VaR is simple, but its measurement is a challenging statistic question.
The article describes the original, definition, types and the basic theory of the financial risk management. And also gives an illustration about modern risk management, it contains main model, method and technology. It makes further discussion about the theory of portfolio selection and combination evaluation. It offered the possible developing tendency of the future financial management. The main studies contain:
(1) The article summarized the definition of the risk from international different research fields at present. It induced seven theory opinions and criticized the different theories and depicted the amount. Now the research has no integrated definition to the contents of the risk. For the different risk source and different risk management goal, different research scholars have different risk measuring methods from the understanding level and studying angle to the risk. The summarizing to the kinds of theories has reflected the people's understanding to the risk incessantly deepen and to be perfect. From the existing risk definition, we emphasize the character of investment risk in the stock investment field. And probe the inherent quality of the risk. It points out that VaR will be more comprehensive and reasonable.
(2) It studies the basic quality of the profit order of stock market in China. It uses SAS and S-plus statistic software to test the relative profit distribution of normal, autocorrelation, heteroskedasticity and independence in common distribution Shanghai stock market. The analysis to the example and result expresses that the profit order has obvious normal character in China stock market. And independence in common distribution hypothesis has been rejected. And the profit order distributes like sophisticated top and thick bottom and has obvious autocorrelation among the order.
(3) It establishes the basic conception and theory analysis frame of VaR. It gives
本文就金融风险管理研究的起源、金融风险的定义及分类、金融风险管理存在的理论基础以及现代金融风险管理的主流模型和方法技术做出了综述。在此基础上，重点研究了证券投资组合选择与组合评价的理论，并提出了金融风险管理研究未来可能的发展方向。主要研究有：
(1) 对目前国内外学术界对风险的定义进行了归纳和综述。归纳出七种学说观点，并对各种学说观点进行了评述和数量刻画。目前学术界对风险的内涵没有统一的定义，针对不同的风险源、风险管理的不同目标，不同的学者对风险的理解和认识程度与研究角度的不同，产生了不同的风险度量方法。通过对各种学说的归纳和总结，反映了人们对风险的认识不断深化、不断完善的递进过程。从现有的风险定义出发，重点分析了证券投资领域投资风险的特殊性，探讨了证券投资风险的本质特征。指出用VaR来描述金融市场风险将更为全面合理。
(2) 对中国股票市场收益率序列基本性质的研究。运用SAS和S-plus统计软件对上海股票市场收益率分布的正态性、自相关性、异方差性、独立同分布性等进行了相应的统计检验。实证分析与检验结果表明，在中国股票市场中，收益率序列具有明显的非正态特征，收益率序列独立同分布的假设被拒绝。收益率序列呈“尖峰厚尾”分布，且序列之间存在着明显的自相关性。
(3) 建立了风险值VaR的基本概念和理论分析框架。给出了服从几何布朗运动的股票和期权的VaR。紧密跟踪学科发展的前沿，对VaR度量的新方法进行了研究。针对模型中要求收益分布服从正态分布的假定，对VaR进行了拓展研究，引入了最坏条件VaR(worst-case VaR，WCVaR)的概念，并给出了它的计算公式。为了检验度量VaR方法的有效性，引入了Kupirc所给出的后验检验统计量，并采用似然比检验的方法，给出了模型有效的拒绝域。
(4) 首次提出了循环修正的组合评价方法。针对目前多指标综合评价方法很多，各种方法的出发点不同，解决问题的思路不同，适用的对象不同等，存在着
With the deepening of global economics integration, investment free port and financial innovation, the financial magnate's volatility and risk are also increased. The financial risk management has become the most important question which is the financial policy and the investor are facing. VaR, that is Value at Risk, as the main way to analyzing, measuring and preventing the financial risk. It is a kind of management way which has just come out to measure the financial risk in the world. It offered us a modern management theoretical conception and thinking. VaR is the method of converting many unmeasurable subjective factors into objective probability numeral value using mathematical statistic and measuring technology. This made the risk obvious and convenient to be managed and controlled. The conception of the VaR is simple, but its measurement is a challenging statistic question.
The article describes the original, definition, types and the basic theory of the financial risk management. And also gives an illustration about modern risk management, it contains main model, method and technology. It makes further discussion about the theory of portfolio selection and combination evaluation. It offered the possible developing tendency of the future financial management. The main studies contain:
(1) The article summarized the definition of the risk from international different research fields at present. It induced seven theory opinions and criticized the different theories and depicted the amount. Now the research has no integrated definition to the contents of the risk. For the different risk source and different risk management goal, different research scholars have different risk measuring methods from the understanding level and studying angle to the risk. The summarizing to the kinds of theories has reflected the people's understanding to the risk incessantly deepen and to be perfect. From the existing risk definition, we emphasize the character of investment risk in the stock investment field. And probe the inherent quality of the risk. It points out that VaR will be more comprehensive and reasonable.
(2) It studies the basic quality of the profit order of stock market in China. It uses SAS and S-plus statistic software to test the relative profit distribution of normal, autocorrelation, heteroskedasticity and independence in common distribution Shanghai stock market. The analysis to the example and result expresses that the profit order has obvious normal character in China stock market. And independence in common distribution hypothesis has been rejected. And the profit order distributes like sophisticated top and thick bottom and has obvious autocorrelation among the order.
(3) It establishes the basic conception and theory analysis frame of VaR. It gives
引文
1．陈学彬 等著．当代金融危机的形成、扩散与防范机制研究[M]．上海：上海财经大学出版社，2001，23-72．
2．钟伟，巴曙松．中国金融风险评估报告[R]．国务院发展研究中心网，www.drcnet.com.cn，2002.
3．杨健．关于国家金融风险防范体系的思考[Z]．国务院发展研究中心网，www.drcnet.com.cn，2002.
4．宋逢明．新世纪曙光照耀下的中国金融工程[Z]．国务院发展研究中心网，www.drcnet.com.cn，2001.
5．陆世敏，戴国强．2002中国金融发展报告[M]．上海：上海财经大学出版社，2002，130-133．
6. Fama E F. Efficient capital market: a review of theory and empirical work[J]. Journal of Finance, 1970, 25(2): 384-417.
7. Sharpe W. Capital asset prices: a theory of market equilibrium under conditions of risk[J]. Journal of Finance, 1964, 19: 425-442.
8. Lintner J. The valuation of risky assets, the selection of risky investment in stock portfolios, capital budgets[J]. Review Economics Statistics, 1965, 47: 13-37.
9. Mossin J. Equilibrium in a capital asset market[J]. Econometric, 1996, 34: 768-783.
10. Ross S A. The arbitrage theory of capital asset pricing[J]. Journal of Economic Theory, 1976, 13: 341-360.
11. Blake F. capital market equilibrium with investment barriers[J]. Journal of Financial Economics, 1972, 45(3): 444-455.
12. Lhabitant F, O Tinguely. Financial risk management: an introduction[J]. Thunderbird Interna-tional Business Review, 2001, 43(3): 343-363.
13．宋逢明．一门新兴的工程学科—金融工程[N]．人民日报．1996，2，17。
14．宋逢明．建立具有中国特色的金融工程新学科[J]．科学中国人，1996，8：13-15．
15．宋逢明．金融科学的工程化[J]．金融研究，1997，7：1-5．
16．朱书尚，李端，周迅宇，汪寿阳．论投资组合与金融优化．对理论研究和实践的分析与反思[J]．管理科学学报，2004，7(6)：1-12．
17. JP Morgan. Risk metrics Technical document[R]. 4th ed. New York: Morgan Guaranty Trust Company, 1996.
18. JP Morgan. Value at risk: The new benchmark for controlling market risk[R]. New York: McGraw-Hill Companies, Inc, 1997.
19. Engle R F. Autoregressive conditional heteroskedasticity with estimates of the??VaRiances of U K inflation[J]. Econometrica, 1982, 31, 987-1008.
20. Bollerslev T. A capitalasset pricing model with time-VaRying coefficients[J]. Journal of Political Economy, 1988, 96: 116-131.
21. Artzner P, Delbaen F, Eber J M, Heath D. Coherent measures of risk[J]. Mathematical Finance, 1999, 9(3): 203-228.
22. Longin M F. Beyond the VaR[J]. Journal of Derivatives, summer 2001, 36-48.
23. Basak S, Shapiro A. Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices[J]. Review of Financial Studies, 2001, 14(2): 371-405.
24. Uryasev S. Conditional Value-at-Risk: Optimization Algorithms and Applications [J]. Financial Engineering News, 2000, 2: 1-5.
25. Brummelimis R. Principal Component Value at Risk[J]. Mathematical Finance, 2002, 12(1): 23-43.
26. Mina J and Ulmer A. Delta-Gamma four ways[R]. Technical report, Risk Metrics Group, 1999.
27. E Jahel, Perraudin W, Sellin P. Value at risk for derivatives[J]. Journal of Derivatives, 1999, 6(3): 7-26.
28. Pownall R A J, Koedijk K G. Capturing downside risk in financial markets: the case of the Asian Crisis[J]. Journal of International Money and Finance, 1999, 18: 853-870.
29. Albanese C, Jackson K, Wiberg P. Hedging with value-at-risk[Z]. www.gloriamundi.org, 2001.
30. Chappell D K. Confidence Intervals for VaR[J]. Financial Engineering News, 1999, 3: 1-2.
31. Jeremy B. Evaluating the Forecasts of Risk Models[Z]. www.gloriamundi.org, 1999.
32. Jean P, Bouchaudand M P. worse fluctutaion method for fast Value at Risk estimates[Z]. www.gloriamundi.org, 1999.
33. David L. Value at Risk Based on the Volatility, Skewness and Kurtosis[Z]. www.gloriamundi, org, 1999.
34. Andrea B, Claudio M. Computing value at risk with high frequency data[J]. Journal of Empirical Finance, 1999, 6: 431-455.
35．王春峰，万海辉，李刚．基于MCMC的金融市场风险VaR的估计[J]．管理科学学报，2000，3(2)：6-12．
36. Nicolas C, Yoshua B. Cost functions and model combination for VaR Based asset allocation using neural networks[Z]. www.iro.umontreal.ca, 2000.
37. J Berkowitz, J O Brien. How Accurate are Value at Risk Models at Commercial Banks [Z]. www.gloriamundi.org, 2002.
38. Mauser H, Rosen D. Beyond VaR: from measuring risk to managing risk[J]. ALGO??Research Quarterly, 1999, 1(2): 5-20.
39. Kaplanski G, Yoram K. VaR Risk Measures versus Traditional Risk Measures An Analysis and Survey[J]. Journal of Risk, 2002, 4(3): 1-34.
40. Dresel T, Hartl R, Johamting L. Risk Capital Allocation Using Value at Risk Limits: The Case of Unpredictable Correlations between Traders' Exposures[Z]. Working Paper, University of Munich, February 2002.
41. Andersen T, Bollerslev T, Diebold F, Labys P. The distribution of exchange rate volatility[Z]. NBER Working Papers, No. 6961, 1999.
42. Jorion P How informative. are Value-at-Risk Disclosures?[Z]. www.gsm.uci.edu/～orion, 2001.
43. Dufie D, Pan J. An overview of value at risk[J]. Journal of Derivatives, 1997, 4(3): 7-9.
44. Irina N K, Svetlozar T R. Value at Risk: Recent Advances[Z]. www.gloriamundi.org, 1999.
45．王春峰．金融市场风险管理[M]．天津大学出版社，2001．
46. Basel Commitee on Banking Supervision. Amendment to the Capital Accord to Incorporate Market Risks[R]. January 1996.
47．海通证券课题组．证券公司风险评价与管理的创新系统—构建PVaR体系[R]．上海联合计划研究课题报告，2002．
48．吴世农，陈斌．风险度量方法与金融资产配置模型的理论和实证研究[J]．经济研究 1999，9：30-38．
49．叶青．基于GARCH和半参数法的VaR模型及其在中国股市风险分析中的应用[J]．统计研究，2000，12：25-29．
50．戴国强，徐龙炳，陆蓉．VaR方法对我国金融风险管理的借鉴及应用[J]．金融研究，2000，7：45-51．
51．刘宇飞．VaR模型及其在金融监管中的应用[J]．经济科学，1999，1：39-50．
52．陈建梁，彭文德．政监会国际组织关于证券公司监管资本框架的新发展[J]．当代经济，2000，3：38-41．
53．黄智猛，曹均华，吴冲锋．VaR风险监管下金融机构的决策模型与分析[J]．系统工程理论方法应用，1999，4：1-6．
54. Vlaar P J G. Value at risk models for Dutch bond portfolios[J]. Journal of Banking and Finance, 2000, 24: 1131-1154.
55. Billio M., Pelizzon L. Value at Risk a multi VaRiate switching regime approach[J]. Journal of Empirical Finance, 2000, 7: 531-554.
56. Hsieh D. Implication of nonlinear dynamics for financial risk management[J]. Journal of Financial and Quantitative Analysis, 1993, 28(1): 41-64.57. Beltratti A., Morana C. Computing value at risk with high frequency data[J]. Journal of Empirical Finance, 1999, 6: 431-455.
58. Artzner P, Delbaen F, Eber J M, Heath D. Coherent measures of risk[J]. Mathematical Finance, 1999, 9(3): 203-228.
59. Jorion P. How informative are Value-at-Risk Disclosures?[Z]. www.gsm.uci.edu/～jorion, 2001.
60. Kevin D. Estimating VaR with Order Statistics [J]. The Journal of Derivatives Spring, 2001, 23-30.
61. Imad A M, Bernard B. A benchmark for measuring bias in estrimated daily value at risk[J]. International Review of Financial Analysis, 2002, 11: 85-100.
62. Malevergne Y, Somette D. General framework for a portfolio theory with non-Gaussian risks and non-linear correlations[Z]. www.gloriamundi.org, 2001.
63. Alexander J M. Extreme Value Theory for Risk Managers[Z]. www.gloriamundi.org, May 17, 1999.
64. Eric B. Multi VaRiate Extremes at Work for Portfolio Risk Measurement[Z]. www.gloriamundi.org, 2002.
65. Frey R, Alexander J M. VaR and expected shortfall in portfolios of dependent credit risks: Conceptual and practical insights[J]. Journal of Banking & Finance, 2002, 26: 1317-1334.
66．詹原瑞，田宏伟．极值理论(EVT)在汇率受险价值(VaR)计算中的应用[J]．系统工程学报，2000，15(1)：3-11．
67．朱国庆，张维，张小薇，敖路．极值理论应用研究进展评析[J]．系统工程学报，2001，16(1)：72-77．
68. NeBci S N, Value at Risk Calculations, Extreme Events, and Tail Estimation[J]. Journal of Derivatives, 2000, 7(3): 23-37.
69．陈衍泰，陈国宏，李美娟．综合评价方法分类及研究进展[J]．管理科学学报，2004，7(2)：69-79．
70．郭显光．一种新的综合评价方法—组合评价法[J]．统计研究，1995，5：56-59．
71. Sharpe W A. Simplified model for portfolio selection analysis[J]. Management Science, 1963, 9: 277-293.
72．朱书尚，李端，周迅宇，汪寿阳．论投资组合与金融优化-对理论研究和实践的 分析与反思[J]．管理科学学报，2004，7(6)：1-12．
73. March J G, Z Shapira. Managerial perspectives on risk and risk taking[J]. Management Science, 1987, 33(11): 1404-1418.
74. Pratt J W. Risk Aversion in the Small and in the Large[J]. Econometrica, 1964, 32: 225-243.
75. Kroll Y, H Levy, H M Markowitz. mean-VaRiance Versus Direct Utility??Maximization[J]. Journal of Finance, 1984, 12(1): 47-61.
76. Bromile R Testing a causal model of corporate risk taking and performance[J]. Academy of Management Journal, 1991, 34(1): 37-59.
77. C A Williams, R M Heins. Risk Management and Insurance[R]. New York: McGraw Hill, 1985.
78. J. S. Rosenbloom. A Case Study in Risk Management[R]. Prentice Hall, 1972.
79. Brockett P L, A Charnes, W Cooper, K H Kwon, T Ruefli. Chance constrained programming models for empirical analyses of mutual fund investment strategies[J]. Decision Sciences, 1992, 3(4): 385-408.
80. Fishburn P C. Foundations of risk measurement, I Risk as a probable loss[J]. Management Science, 30(4): 396-406.
81. Markowitz H M. portfolio Selection: Effcient diversification ofnInvestment[M]. New York: John Wiley & Sons, 1959.
82. Collins J M, T W Ruefli. Strategicbrisk: An ordinal approach[J]. Management Science, 1992, 38(12): 1707-1731.
83．叶青，易丹辉．中国证券市场风险分析基本框机架的研究[J]．金融研究，2000，6．
84. Philippe J. Value at Risk: The New Benchmark for Controlling Market Risk[R]. Chicago: Irwin Professional Publishong, 1996.
85．E E Peter著，王小东译．资本市场的混沌与秩序[M]．经济科学出版社，1999．
86. Mandelbrot B B. Fractional brownian motions, fractional noises and applications [J]. SIAM Review, 1968, 10(4): 422-437.
87. Mandelbrot B B. Limit theorems on the self-normalized range for weakly and strongly dependent processes[J]. Z. Wahrscheinlichkeits theorie reverw. Gebiete, 1975, 31: 271-285.
88．朱世武．基于SAS系统的金融计算[M]．清华大学出版社，2004．
89．高惠璇，张庆峰，张利华，孙明举．SAS系统与市场调查数据分析[M]．北京大学概率统计系，1999．
90．方兆本，缪柏其．随机过程[M]．科学出版社，2004．
91．Terence C Mills著，俞卓箐译．金融时间序列的经济计量学模型(第二版)[M]．经济科学出版社，2002．
92. Alexander C. Risk management and analysis. Vol. 1: Measuring and modeling financial risk[R]. New York: John Wiley & Sons Ltd, 1998.
93. Alexander C. The handbook of risk management and analysis. Volatility and Correlation Forecasting[R]. New York: John Wiley & Sons Ltd, 1996.
94. Bolleslev T. Generalized autoregressive conditional heteroskedasticity[J]. Journal of Econometrics, 1986, 31: 307-327.
95. Zakoian J M. Threshold heteroskedastic models[J]. Journal of Economic Dynamics??and Control, 1994, 18: 931-955.
96. Higgins M L, Bera A K. A class of nonlinear ARCH models[J].International Economic Review, 1992,33(1): 137-158.
97. Schwert G W. Why does stock market volatility change over time?[J] Journal of Finance, 1989,44: 1115-1153.
98. Duan J C. Augmented GARCH(p,q) process and its diffusion limit[J] Journal of Econometrics, 1997, 79: 97-127.
99. Ding Zhuanxin, Granger C W J. Modeling volatility persistence of speculative returns: anew approach[J]. Journal of Econometrics, 1996, 73: 185-215.
100.Baillie R F, Bollerslev T, Mikkelsen H O. Fractionally integrated generalized autoregressive conditional heteroskedasticity[J].Journal of Econometrics, 1996, 74: 3-30.
101.Nelson D B. Conditional heteroskedasticity in asset returns: a new approach[J]. Econometrica, 1991, 59(2): 347-370.
102.Bollerslev T, Mikkelsen H O. Modeling and pricing long memory in stock market volatility [J]. Journal of Econometrics, 1996, 73: 151-184.
103.Geweke J. Modeling the persistence of conditional VaRiances: a comment[J]. Econometric Revews, 1986, 5: 57-61.
104.Engle R.F, Ng V K. Measuring and testing the impact of new on volatility [J]. Journal of Finance, 1993,48: 1749-1778.
105.Nelson D B. Conditional heteroskedasticity in asset returns: a new approach[J]. Econometrica, 1991, 59(2): 347-370.
106.Engle R F, Bollerslev T. Modeling the persistence of conditional VaRiances[J]. Econometric Reviews, 1986, 5: 81-87.
107.Engle R F, Lilien D M, Robins R P. Estimating time-VaRying risk premia in the term structure: the ARCH-M model[J].Econometrica, 1987, 55(2): 391-407.
108.Hansen L. Large sample properties of generalized method of moments estimators [J].Econometrica, 1982, 50: 1269-1287.
109.Box G E P, Pierce D A. Distribution of residual autocorrelations in autoregressive -integrated moving average time series models[J]. J. Amer. Statist. Assoc, 1970, 65: 1509-1526.
110. Ljung G M, Box G M P. On a measure of lack of fit in time series models[J]. Biometrika, 1978, 65: 297-303.
111.Robinson P M. Testing for strong serial correlation and dynamic conditional heteroskedaticity in multiple regression[J]. Journal of Econometrics, 1991, 47: 67-84.
112.Hsieh D. Implication of nonlinear dynamics for financial risk management[J]. Journal of Financial and Quantitative Analysis, 1993,28(1): 41-64.
113. Wilson T. Plugging the GAP[J]. Risk, 1994, 7(10): 74-80.
114. Martin L H. An optimal local bandwidth selector for kernel density estimation[J]. Journal of Statistical Planning and Inference, 1999, 77: 37-50.
115. Kyung D K, Jun H H. Comparative Study of Flood Quintiles Estimation by Nonparametric Model[J]. Journal of Hydrology, 2002, 206: 176-193.
116. Reza M. Efficient nonparametric estimation of a distribution function[J]. Computational Statistics & Data Analysis, 2002, 39: 75-95.
117. Jef C, Jozef V D. Nonparametric tail estimation using a double bootstrap method[J]. Computational. Statistics & Data Analysis, 1999, 29: 191-211.
118. Bertvan E. On the expansion of the mean integrated squared error of a kernel density estimator[J]. Statistics & Probability Letters, 2001, 52: 441-450.
119. Hull J, White A. The pricing of options on assets with stochastic volatilities[J]. Journal of Finance, 1987, 42: 1102-1131.
120. Boyle P. Options: A Monte Carlo approach[J]. Journal of Financial Economics, 1977, 4: 323-338.
121. Moro B. The full Monte Carlo[J]. Risk, 1995, 8: 22-28.
122. Jamshidian F, Zhu Y. Scenario simulation: Theory and methodology[J]. Finance and Stocgastics, 1997, 1: 43-67.
123. Geman S, Geman D. Stochastic relaxation, Gibbs distribution and the Baysian restoration of images[J]. IEEE Transactions on Pattern Analysis Machine Intelligence, 984, 6: 721-741.
124．王春峰，万海晖，李刚．基于MCMC的金融市场风险VaR的估计[J]．管理科学学报，2000，3(2)：56-64．
125．张尧庭，方开泰．多元统计分析引论[M]．科学出版社，1997．
126．王春峰等．金融市场风险测量模型—VaR[J]．系统工程学报，2000，15(1)：67-75．
127. Wison T. Plugging the GAP[J]. Risk, 1994, 7(10): 74-80.
128. Alexander G J, Baptista A M. Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-VaRiance Analysis[J]. Journal of Economic Dynamics and Control, 2002, 26: 1159-1193.
129. Laurent E G, Maksim O, Francois O. Worst-case value-at-risk and robust portfolio optimization: a conic programming approach[J]. Operation Research of Informs, 2003, 51(4): 543-556.
130. Kupiec P H. Techniques for verifying the accuracy of risk measurement models[J]. The Journal of Derivatives, 1995, 75(2): 73-84.
131．邱东．多指标综合评价方法的系统分析[M]．中国统计出版社，1991．
132．徐强．组合评价法研究[J]．江苏统计，2002，10：10-12．
133．张尧庭，张璋．几种选取部分代表性指标的统计方法[J]．统计研究，1990，1：??12-16．
134．胡永宏，贺思辉．综合评价方法[J]．科学出版社，2000．
135．梅国平．上市公司及证券投资基金绩效评价-方法与实证[D]．复旦大学博士后工作报告，2003．
136. H wang, Yoon K S. Multiple Attribute Decision Making[M]. Spring Verlag, Berlin, 1981.
137．欧俊豪，马逢时．城市综合经济实力的主成分分析[J1．数理统计与管理，1999，18(3)：13-18．
138．邓艳红，李容．重庆市社会经济发展的实证分析[J]．数理统计与管理，2002，21(6)：11-14．
139．郭显光．一种新的综合评价方法—组合评价法[J]．统计研究，1995，5：56-59．
140．王星．非参数统计[M]．中国人民大学出版社，2005．
141．施锡铨，范正绮．数据分析方法[M]．上海财经大学出版社，1997．
142．史树中．诺贝尔经济学奖与数学[J]．清华大学出版社，2002．
143．平新乔．微观经济学十八讲[J]．北京大学出版社，2001．
144. Mao J C T. Essentials of portfolio diversification strategy[J]. Journal of Finance, 1970, 25(5), 1109-1121.
145. Tanaka H, Guo P. Portfolio selection based on upper and lower exponential possibility distributions[J]. European Journal of Operational Research, 1999, 114: 115-126.
146. Konno K, Yamazaki H. Mean absolute deviation portfolio optimization model and its application to Tokyo stock market[J]. Management Science, 1991, 37: 519-531.
147. Konno H, Li J. An internationally diversified investment using a sotckbond integrated portfolio model[J]. International Journal of Theoretical and Applied Finance, 1990, 1: 145-160.
148. Merton R C. Lifetime portfolio selection under uncertainty: The continuous time case[J]. Review of Economics and Statistics, 1969, 51, 247-257.
149. Steuer R E. Algorithm for linear programming problems with interval objective function coefficients[J]. Mathematics of Operational Research, 1981, 6: 333-348.
150. Sengupta, J. K., Portfolio decisions as games, International Journal of Systems Science, Vol. 20, pp. 1323-1334, 1989
151. Konno H, Wijayanayake A. Mean absolute deviation portfolio optimization model under transaction costs[J]. Journal of the Operations Research Society of Japan, 1999, 42, 422-435.
152. Kane A. Skewness preference and portfolio choice[J]. Journal of Financial and Quantitative Analysis, 1982, 17: 15-26.
153. Chunhachinda P, Dandapani K, Hamid S, Prakash A J. Portfolio selection and??skewness: evidence from international stock markets[J].Journal of Banking and Finance, 1997,21: 143-167.
154.Roy A D. Safety-first and the holding of assets[J].Econometrics, 1952, 20: 431-449.
155.Telser L G.. Safety first and hedging[J].Review of Economic Studies, 1955, 23: 1-16.
156.Mossin J. Optimal muli-period portfolio policies [J] Journal of Business, 1968, 41: 215-229.
157.Merton R C. Lifetime portfolio selection under uncertainty: The continuous time case[J] .Review of Economics and Statistics, 1969, 51: 247-257.
158.Chen A, Jen F C, Zionts S. The optimal portfolio revision policy[J] Journal of Business, 1971,44: 51-61.
159.Hakansson N H. Multi-period mean-VaRiance analysis: Toward a general theory of portfolio choice [J] Journal of Finance, 1971, 26: 857-884.
160.Elton E J, Gruber M J. On the optimality of some multiperiod portfolio selection criteria[J] Journal of Business, 1974, 7: 231-243.
161.Dumas B, Luciano E. An exact solution to a dynamic portfolio choice problem under transaction cost[J] Journal of Finance, 1991, 46: 577-595.
162.Zhou X Y, Li D. Continuous-time mean-VaRiance portfolio selection: a stochastic LQ framework[J].Applied Mathematics and Optimization, 2000, 42: 19-33.
163.Li D, Ng W K. Optimal dynamic portfolio selection: multi-period mean VaRiance formulation[J].Mathematical Finance, 2000, 10: 387-406.
164.Cover T M. Universal Portfolios [J].Mathematical Finance, 1991, 1: 1-29.
165.Hembold D P, Schapire R E, Spriner Y, Warmuth M K. On-line portfolio selectioin using multiplicative updates[J].Mathematical Finance, 1998, 8: 325-347.
166.Zadeh L A. Fuzzy sets [J]. Information and Control,1965, 8: 338-353.
167.Bellman R, Zadeh L A. Decision making in a fuzzy environment [J]. Manage- ment Science, 1970, 17: 141-164.
168.Watada J. Fuzzy portfolio model for decision making in investment, in Y. Yoshida(eds.), Dynamical Asspects in Fuzzy Decision Making[J]. Physica Verlag, Heidelberg, 2001, 141-162.
2．钟伟，巴曙松．中国金融风险评估报告[R]．国务院发展研究中心网，www.drcnet.com.cn，2002.
3．杨健．关于国家金融风险防范体系的思考[Z]．国务院发展研究中心网，www.drcnet.com.cn，2002.
4．宋逢明．新世纪曙光照耀下的中国金融工程[Z]．国务院发展研究中心网，www.drcnet.com.cn，2001.
5．陆世敏，戴国强．2002中国金融发展报告[M]．上海：上海财经大学出版社，2002，130-133．
6. Fama E F. Efficient capital market: a review of theory and empirical work[J]. Journal of Finance, 1970, 25(2): 384-417.
7. Sharpe W. Capital asset prices: a theory of market equilibrium under conditions of risk[J]. Journal of Finance, 1964, 19: 425-442.
8. Lintner J. The valuation of risky assets, the selection of risky investment in stock portfolios, capital budgets[J]. Review Economics Statistics, 1965, 47: 13-37.
9. Mossin J. Equilibrium in a capital asset market[J]. Econometric, 1996, 34: 768-783.
10. Ross S A. The arbitrage theory of capital asset pricing[J]. Journal of Economic Theory, 1976, 13: 341-360.
11. Blake F. capital market equilibrium with investment barriers[J]. Journal of Financial Economics, 1972, 45(3): 444-455.
12. Lhabitant F, O Tinguely. Financial risk management: an introduction[J]. Thunderbird Interna-tional Business Review, 2001, 43(3): 343-363.
13．宋逢明．一门新兴的工程学科—金融工程[N]．人民日报．1996，2，17。
14．宋逢明．建立具有中国特色的金融工程新学科[J]．科学中国人，1996，8：13-15．
15．宋逢明．金融科学的工程化[J]．金融研究，1997，7：1-5．
16．朱书尚，李端，周迅宇，汪寿阳．论投资组合与金融优化．对理论研究和实践的分析与反思[J]．管理科学学报，2004，7(6)：1-12．
17. JP Morgan. Risk metrics Technical document[R]. 4th ed. New York: Morgan Guaranty Trust Company, 1996.
18. JP Morgan. Value at risk: The new benchmark for controlling market risk[R]. New York: McGraw-Hill Companies, Inc, 1997.
19. Engle R F. Autoregressive conditional heteroskedasticity with estimates of the??VaRiances of U K inflation[J]. Econometrica, 1982, 31, 987-1008.
20. Bollerslev T. A capitalasset pricing model with time-VaRying coefficients[J]. Journal of Political Economy, 1988, 96: 116-131.
21. Artzner P, Delbaen F, Eber J M, Heath D. Coherent measures of risk[J]. Mathematical Finance, 1999, 9(3): 203-228.
22. Longin M F. Beyond the VaR[J]. Journal of Derivatives, summer 2001, 36-48.
23. Basak S, Shapiro A. Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices[J]. Review of Financial Studies, 2001, 14(2): 371-405.
24. Uryasev S. Conditional Value-at-Risk: Optimization Algorithms and Applications [J]. Financial Engineering News, 2000, 2: 1-5.
25. Brummelimis R. Principal Component Value at Risk[J]. Mathematical Finance, 2002, 12(1): 23-43.
26. Mina J and Ulmer A. Delta-Gamma four ways[R]. Technical report, Risk Metrics Group, 1999.
27. E Jahel, Perraudin W, Sellin P. Value at risk for derivatives[J]. Journal of Derivatives, 1999, 6(3): 7-26.
28. Pownall R A J, Koedijk K G. Capturing downside risk in financial markets: the case of the Asian Crisis[J]. Journal of International Money and Finance, 1999, 18: 853-870.
29. Albanese C, Jackson K, Wiberg P. Hedging with value-at-risk[Z]. www.gloriamundi.org, 2001.
30. Chappell D K. Confidence Intervals for VaR[J]. Financial Engineering News, 1999, 3: 1-2.
31. Jeremy B. Evaluating the Forecasts of Risk Models[Z]. www.gloriamundi.org, 1999.
32. Jean P, Bouchaudand M P. worse fluctutaion method for fast Value at Risk estimates[Z]. www.gloriamundi.org, 1999.
33. David L. Value at Risk Based on the Volatility, Skewness and Kurtosis[Z]. www.gloriamundi, org, 1999.
34. Andrea B, Claudio M. Computing value at risk with high frequency data[J]. Journal of Empirical Finance, 1999, 6: 431-455.
35．王春峰，万海辉，李刚．基于MCMC的金融市场风险VaR的估计[J]．管理科学学报，2000，3(2)：6-12．
36. Nicolas C, Yoshua B. Cost functions and model combination for VaR Based asset allocation using neural networks[Z]. www.iro.umontreal.ca, 2000.
37. J Berkowitz, J O Brien. How Accurate are Value at Risk Models at Commercial Banks [Z]. www.gloriamundi.org, 2002.
38. Mauser H, Rosen D. Beyond VaR: from measuring risk to managing risk[J]. ALGO??Research Quarterly, 1999, 1(2): 5-20.
39. Kaplanski G, Yoram K. VaR Risk Measures versus Traditional Risk Measures An Analysis and Survey[J]. Journal of Risk, 2002, 4(3): 1-34.
40. Dresel T, Hartl R, Johamting L. Risk Capital Allocation Using Value at Risk Limits: The Case of Unpredictable Correlations between Traders' Exposures[Z]. Working Paper, University of Munich, February 2002.
41. Andersen T, Bollerslev T, Diebold F, Labys P. The distribution of exchange rate volatility[Z]. NBER Working Papers, No. 6961, 1999.
42. Jorion P How informative. are Value-at-Risk Disclosures?[Z]. www.gsm.uci.edu/～orion, 2001.
43. Dufie D, Pan J. An overview of value at risk[J]. Journal of Derivatives, 1997, 4(3): 7-9.
44. Irina N K, Svetlozar T R. Value at Risk: Recent Advances[Z]. www.gloriamundi.org, 1999.
45．王春峰．金融市场风险管理[M]．天津大学出版社，2001．
46. Basel Commitee on Banking Supervision. Amendment to the Capital Accord to Incorporate Market Risks[R]. January 1996.
47．海通证券课题组．证券公司风险评价与管理的创新系统—构建PVaR体系[R]．上海联合计划研究课题报告，2002．
48．吴世农，陈斌．风险度量方法与金融资产配置模型的理论和实证研究[J]．经济研究 1999，9：30-38．
49．叶青．基于GARCH和半参数法的VaR模型及其在中国股市风险分析中的应用[J]．统计研究，2000，12：25-29．
50．戴国强，徐龙炳，陆蓉．VaR方法对我国金融风险管理的借鉴及应用[J]．金融研究，2000，7：45-51．
51．刘宇飞．VaR模型及其在金融监管中的应用[J]．经济科学，1999，1：39-50．
52．陈建梁，彭文德．政监会国际组织关于证券公司监管资本框架的新发展[J]．当代经济，2000，3：38-41．
53．黄智猛，曹均华，吴冲锋．VaR风险监管下金融机构的决策模型与分析[J]．系统工程理论方法应用，1999，4：1-6．
54. Vlaar P J G. Value at risk models for Dutch bond portfolios[J]. Journal of Banking and Finance, 2000, 24: 1131-1154.
55. Billio M., Pelizzon L. Value at Risk a multi VaRiate switching regime approach[J]. Journal of Empirical Finance, 2000, 7: 531-554.
56. Hsieh D. Implication of nonlinear dynamics for financial risk management[J]. Journal of Financial and Quantitative Analysis, 1993, 28(1): 41-64.57. Beltratti A., Morana C. Computing value at risk with high frequency data[J]. Journal of Empirical Finance, 1999, 6: 431-455.
58. Artzner P, Delbaen F, Eber J M, Heath D. Coherent measures of risk[J]. Mathematical Finance, 1999, 9(3): 203-228.
59. Jorion P. How informative are Value-at-Risk Disclosures?[Z]. www.gsm.uci.edu/～jorion, 2001.
60. Kevin D. Estimating VaR with Order Statistics [J]. The Journal of Derivatives Spring, 2001, 23-30.
61. Imad A M, Bernard B. A benchmark for measuring bias in estrimated daily value at risk[J]. International Review of Financial Analysis, 2002, 11: 85-100.
62. Malevergne Y, Somette D. General framework for a portfolio theory with non-Gaussian risks and non-linear correlations[Z]. www.gloriamundi.org, 2001.
63. Alexander J M. Extreme Value Theory for Risk Managers[Z]. www.gloriamundi.org, May 17, 1999.
64. Eric B. Multi VaRiate Extremes at Work for Portfolio Risk Measurement[Z]. www.gloriamundi.org, 2002.
65. Frey R, Alexander J M. VaR and expected shortfall in portfolios of dependent credit risks: Conceptual and practical insights[J]. Journal of Banking & Finance, 2002, 26: 1317-1334.
66．詹原瑞，田宏伟．极值理论(EVT)在汇率受险价值(VaR)计算中的应用[J]．系统工程学报，2000，15(1)：3-11．
67．朱国庆，张维，张小薇，敖路．极值理论应用研究进展评析[J]．系统工程学报，2001，16(1)：72-77．
68. NeBci S N, Value at Risk Calculations, Extreme Events, and Tail Estimation[J]. Journal of Derivatives, 2000, 7(3): 23-37.
69．陈衍泰，陈国宏，李美娟．综合评价方法分类及研究进展[J]．管理科学学报，2004，7(2)：69-79．
70．郭显光．一种新的综合评价方法—组合评价法[J]．统计研究，1995，5：56-59．
71. Sharpe W A. Simplified model for portfolio selection analysis[J]. Management Science, 1963, 9: 277-293.
72．朱书尚，李端，周迅宇，汪寿阳．论投资组合与金融优化-对理论研究和实践的 分析与反思[J]．管理科学学报，2004，7(6)：1-12．
73. March J G, Z Shapira. Managerial perspectives on risk and risk taking[J]. Management Science, 1987, 33(11): 1404-1418.
74. Pratt J W. Risk Aversion in the Small and in the Large[J]. Econometrica, 1964, 32: 225-243.
75. Kroll Y, H Levy, H M Markowitz. mean-VaRiance Versus Direct Utility??Maximization[J]. Journal of Finance, 1984, 12(1): 47-61.
76. Bromile R Testing a causal model of corporate risk taking and performance[J]. Academy of Management Journal, 1991, 34(1): 37-59.
77. C A Williams, R M Heins. Risk Management and Insurance[R]. New York: McGraw Hill, 1985.
78. J. S. Rosenbloom. A Case Study in Risk Management[R]. Prentice Hall, 1972.
79. Brockett P L, A Charnes, W Cooper, K H Kwon, T Ruefli. Chance constrained programming models for empirical analyses of mutual fund investment strategies[J]. Decision Sciences, 1992, 3(4): 385-408.
80. Fishburn P C. Foundations of risk measurement, I Risk as a probable loss[J]. Management Science, 30(4): 396-406.
81. Markowitz H M. portfolio Selection: Effcient diversification ofnInvestment[M]. New York: John Wiley & Sons, 1959.
82. Collins J M, T W Ruefli. Strategicbrisk: An ordinal approach[J]. Management Science, 1992, 38(12): 1707-1731.
83．叶青，易丹辉．中国证券市场风险分析基本框机架的研究[J]．金融研究，2000，6．
84. Philippe J. Value at Risk: The New Benchmark for Controlling Market Risk[R]. Chicago: Irwin Professional Publishong, 1996.
85．E E Peter著，王小东译．资本市场的混沌与秩序[M]．经济科学出版社，1999．
86. Mandelbrot B B. Fractional brownian motions, fractional noises and applications [J]. SIAM Review, 1968, 10(4): 422-437.
87. Mandelbrot B B. Limit theorems on the self-normalized range for weakly and strongly dependent processes[J]. Z. Wahrscheinlichkeits theorie reverw. Gebiete, 1975, 31: 271-285.
88．朱世武．基于SAS系统的金融计算[M]．清华大学出版社，2004．
89．高惠璇，张庆峰，张利华，孙明举．SAS系统与市场调查数据分析[M]．北京大学概率统计系，1999．
90．方兆本，缪柏其．随机过程[M]．科学出版社，2004．
91．Terence C Mills著，俞卓箐译．金融时间序列的经济计量学模型(第二版)[M]．经济科学出版社，2002．
92. Alexander C. Risk management and analysis. Vol. 1: Measuring and modeling financial risk[R]. New York: John Wiley & Sons Ltd, 1998.
93. Alexander C. The handbook of risk management and analysis. Volatility and Correlation Forecasting[R]. New York: John Wiley & Sons Ltd, 1996.
94. Bolleslev T. Generalized autoregressive conditional heteroskedasticity[J]. Journal of Econometrics, 1986, 31: 307-327.
95. Zakoian J M. Threshold heteroskedastic models[J]. Journal of Economic Dynamics??and Control, 1994, 18: 931-955.
96. Higgins M L, Bera A K. A class of nonlinear ARCH models[J].International Economic Review, 1992,33(1): 137-158.
97. Schwert G W. Why does stock market volatility change over time?[J] Journal of Finance, 1989,44: 1115-1153.
98. Duan J C. Augmented GARCH(p,q) process and its diffusion limit[J] Journal of Econometrics, 1997, 79: 97-127.
99. Ding Zhuanxin, Granger C W J. Modeling volatility persistence of speculative returns: anew approach[J]. Journal of Econometrics, 1996, 73: 185-215.
100.Baillie R F, Bollerslev T, Mikkelsen H O. Fractionally integrated generalized autoregressive conditional heteroskedasticity[J].Journal of Econometrics, 1996, 74: 3-30.
101.Nelson D B. Conditional heteroskedasticity in asset returns: a new approach[J]. Econometrica, 1991, 59(2): 347-370.
102.Bollerslev T, Mikkelsen H O. Modeling and pricing long memory in stock market volatility [J]. Journal of Econometrics, 1996, 73: 151-184.
103.Geweke J. Modeling the persistence of conditional VaRiances: a comment[J]. Econometric Revews, 1986, 5: 57-61.
104.Engle R.F, Ng V K. Measuring and testing the impact of new on volatility [J]. Journal of Finance, 1993,48: 1749-1778.
105.Nelson D B. Conditional heteroskedasticity in asset returns: a new approach[J]. Econometrica, 1991, 59(2): 347-370.
106.Engle R F, Bollerslev T. Modeling the persistence of conditional VaRiances[J]. Econometric Reviews, 1986, 5: 81-87.
107.Engle R F, Lilien D M, Robins R P. Estimating time-VaRying risk premia in the term structure: the ARCH-M model[J].Econometrica, 1987, 55(2): 391-407.
108.Hansen L. Large sample properties of generalized method of moments estimators [J].Econometrica, 1982, 50: 1269-1287.
109.Box G E P, Pierce D A. Distribution of residual autocorrelations in autoregressive -integrated moving average time series models[J]. J. Amer. Statist. Assoc, 1970, 65: 1509-1526.
110. Ljung G M, Box G M P. On a measure of lack of fit in time series models[J]. Biometrika, 1978, 65: 297-303.
111.Robinson P M. Testing for strong serial correlation and dynamic conditional heteroskedaticity in multiple regression[J]. Journal of Econometrics, 1991, 47: 67-84.
112.Hsieh D. Implication of nonlinear dynamics for financial risk management[J]. Journal of Financial and Quantitative Analysis, 1993,28(1): 41-64.
113. Wilson T. Plugging the GAP[J]. Risk, 1994, 7(10): 74-80.
114. Martin L H. An optimal local bandwidth selector for kernel density estimation[J]. Journal of Statistical Planning and Inference, 1999, 77: 37-50.
115. Kyung D K, Jun H H. Comparative Study of Flood Quintiles Estimation by Nonparametric Model[J]. Journal of Hydrology, 2002, 206: 176-193.
116. Reza M. Efficient nonparametric estimation of a distribution function[J]. Computational Statistics & Data Analysis, 2002, 39: 75-95.
117. Jef C, Jozef V D. Nonparametric tail estimation using a double bootstrap method[J]. Computational. Statistics & Data Analysis, 1999, 29: 191-211.
118. Bertvan E. On the expansion of the mean integrated squared error of a kernel density estimator[J]. Statistics & Probability Letters, 2001, 52: 441-450.
119. Hull J, White A. The pricing of options on assets with stochastic volatilities[J]. Journal of Finance, 1987, 42: 1102-1131.
120. Boyle P. Options: A Monte Carlo approach[J]. Journal of Financial Economics, 1977, 4: 323-338.
121. Moro B. The full Monte Carlo[J]. Risk, 1995, 8: 22-28.
122. Jamshidian F, Zhu Y. Scenario simulation: Theory and methodology[J]. Finance and Stocgastics, 1997, 1: 43-67.
123. Geman S, Geman D. Stochastic relaxation, Gibbs distribution and the Baysian restoration of images[J]. IEEE Transactions on Pattern Analysis Machine Intelligence, 984, 6: 721-741.
124．王春峰，万海晖，李刚．基于MCMC的金融市场风险VaR的估计[J]．管理科学学报，2000，3(2)：56-64．
125．张尧庭，方开泰．多元统计分析引论[M]．科学出版社，1997．
126．王春峰等．金融市场风险测量模型—VaR[J]．系统工程学报，2000，15(1)：67-75．
127. Wison T. Plugging the GAP[J]. Risk, 1994, 7(10): 74-80.
128. Alexander G J, Baptista A M. Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-VaRiance Analysis[J]. Journal of Economic Dynamics and Control, 2002, 26: 1159-1193.
129. Laurent E G, Maksim O, Francois O. Worst-case value-at-risk and robust portfolio optimization: a conic programming approach[J]. Operation Research of Informs, 2003, 51(4): 543-556.
130. Kupiec P H. Techniques for verifying the accuracy of risk measurement models[J]. The Journal of Derivatives, 1995, 75(2): 73-84.
131．邱东．多指标综合评价方法的系统分析[M]．中国统计出版社，1991．
132．徐强．组合评价法研究[J]．江苏统计，2002，10：10-12．
133．张尧庭，张璋．几种选取部分代表性指标的统计方法[J]．统计研究，1990，1：??12-16．
134．胡永宏，贺思辉．综合评价方法[J]．科学出版社，2000．
135．梅国平．上市公司及证券投资基金绩效评价-方法与实证[D]．复旦大学博士后工作报告，2003．
136. H wang, Yoon K S. Multiple Attribute Decision Making[M]. Spring Verlag, Berlin, 1981.
137．欧俊豪，马逢时．城市综合经济实力的主成分分析[J1．数理统计与管理，1999，18(3)：13-18．
138．邓艳红，李容．重庆市社会经济发展的实证分析[J]．数理统计与管理，2002，21(6)：11-14．
139．郭显光．一种新的综合评价方法—组合评价法[J]．统计研究，1995，5：56-59．
140．王星．非参数统计[M]．中国人民大学出版社，2005．
141．施锡铨，范正绮．数据分析方法[M]．上海财经大学出版社，1997．
142．史树中．诺贝尔经济学奖与数学[J]．清华大学出版社，2002．
143．平新乔．微观经济学十八讲[J]．北京大学出版社，2001．
144. Mao J C T. Essentials of portfolio diversification strategy[J]. Journal of Finance, 1970, 25(5), 1109-1121.
145. Tanaka H, Guo P. Portfolio selection based on upper and lower exponential possibility distributions[J]. European Journal of Operational Research, 1999, 114: 115-126.
146. Konno K, Yamazaki H. Mean absolute deviation portfolio optimization model and its application to Tokyo stock market[J]. Management Science, 1991, 37: 519-531.
147. Konno H, Li J. An internationally diversified investment using a sotckbond integrated portfolio model[J]. International Journal of Theoretical and Applied Finance, 1990, 1: 145-160.
148. Merton R C. Lifetime portfolio selection under uncertainty: The continuous time case[J]. Review of Economics and Statistics, 1969, 51, 247-257.
149. Steuer R E. Algorithm for linear programming problems with interval objective function coefficients[J]. Mathematics of Operational Research, 1981, 6: 333-348.
150. Sengupta, J. K., Portfolio decisions as games, International Journal of Systems Science, Vol. 20, pp. 1323-1334, 1989
151. Konno H, Wijayanayake A. Mean absolute deviation portfolio optimization model under transaction costs[J]. Journal of the Operations Research Society of Japan, 1999, 42, 422-435.
152. Kane A. Skewness preference and portfolio choice[J]. Journal of Financial and Quantitative Analysis, 1982, 17: 15-26.
153. Chunhachinda P, Dandapani K, Hamid S, Prakash A J. Portfolio selection and??skewness: evidence from international stock markets[J].Journal of Banking and Finance, 1997,21: 143-167.
154.Roy A D. Safety-first and the holding of assets[J].Econometrics, 1952, 20: 431-449.
155.Telser L G.. Safety first and hedging[J].Review of Economic Studies, 1955, 23: 1-16.
156.Mossin J. Optimal muli-period portfolio policies [J] Journal of Business, 1968, 41: 215-229.
157.Merton R C. Lifetime portfolio selection under uncertainty: The continuous time case[J] .Review of Economics and Statistics, 1969, 51: 247-257.
158.Chen A, Jen F C, Zionts S. The optimal portfolio revision policy[J] Journal of Business, 1971,44: 51-61.
159.Hakansson N H. Multi-period mean-VaRiance analysis: Toward a general theory of portfolio choice [J] Journal of Finance, 1971, 26: 857-884.
160.Elton E J, Gruber M J. On the optimality of some multiperiod portfolio selection criteria[J] Journal of Business, 1974, 7: 231-243.
161.Dumas B, Luciano E. An exact solution to a dynamic portfolio choice problem under transaction cost[J] Journal of Finance, 1991, 46: 577-595.
162.Zhou X Y, Li D. Continuous-time mean-VaRiance portfolio selection: a stochastic LQ framework[J].Applied Mathematics and Optimization, 2000, 42: 19-33.
163.Li D, Ng W K. Optimal dynamic portfolio selection: multi-period mean VaRiance formulation[J].Mathematical Finance, 2000, 10: 387-406.
164.Cover T M. Universal Portfolios [J].Mathematical Finance, 1991, 1: 1-29.
165.Hembold D P, Schapire R E, Spriner Y, Warmuth M K. On-line portfolio selectioin using multiplicative updates[J].Mathematical Finance, 1998, 8: 325-347.
166.Zadeh L A. Fuzzy sets [J]. Information and Control,1965, 8: 338-353.
167.Bellman R, Zadeh L A. Decision making in a fuzzy environment [J]. Manage- ment Science, 1970, 17: 141-164.
168.Watada J. Fuzzy portfolio model for decision making in investment, in Y. Yoshida(eds.), Dynamical Asspects in Fuzzy Decision Making[J]. Physica Verlag, Heidelberg, 2001, 141-162.