金融资产收益相关性及持续性研究
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摘要
金融资产收益相关性及持续性研究是金融工程研究领域的中心,准确度量资产收益之间的相关性及持续性是探索资本市场运行机理和实务操作的关键。为此,将统计物理学和多元统计学中的有关理论及金融计量模型与金融领域的现实问题相结合取得了如下成果:
1.以统计物理学中的随机相关矩阵特征值概率密度为理论依据,构建了收益相关矩阵选取方法,从而解决了收益相关矩阵优选问题。实证检验显示,按由该方法所选取的收益相关矩阵配置资产可得到优质的有效前沿。
2.以多元统计学中的Wishart概率密度为理论依据,推导出相关系数的修正模型,该模型剔除了样本容量效应,使相关性度量更为准确可靠。实证结果显示,该模型具有较高的资产配置效率。
3.基于协同持续思想通过GARCH模型技术构建了动态投资组合模型,该模型可捕捉到金融资产收益的局部波动,达到控制风险扩散的目的。实证显示,按该模型配置资产可控制组合收益率在较小范围内波动,也可得较高夏普比。
4.提出风险溢出发生期及风险溢出强度两个概念,并构建了相应数学模型。同时,基于该模型进行了实证研究,结果显示,沪市影响深市的程度较深市影响沪市的程度大,且它们之间的风险溢出在大约3分钟之内完成,这一研究结果与实际吻合。
5.将统计物理学中的公因子提取法运用于资本资产定价方面,提出了CAPM修正模型。实证结果显示该模型较原模型具有较高的定价能力。
上述理论成果依次在论文五个主体章节中展开讨论,这些研究成果均遵循从理论依据到方法构建、模型提出,再到实证检验的研究思路,从而确保了研究工作的科学性和实用性。
It is most important step to study on the correlation and persistence of the financial capital return,especially,is most crucial work measuring accuratelly the correlation and persistence to explore the mechanism and operation of the capital market. To this end, by applying the theory of statistical physics and multiple-statistics and the model for financial measures to the practical problems of financia field, the achievements are as follows:
1. The method to discerning the best correlation matrix is obtainded by the random matrix eigenvalue probability density function in statistical physics solving the matrix optimization. Empirical tests show that the efficient frontier may be bettler by the method .
2. Based on Wishart probability distribution of multiple statistics, the revised model of the correlation coefficient is derived so that the sample pool doubt disappear and so the correlation coefficient becomes an accurate measure tool.
3. After considering the Co-persistence thought, the dynamic portfolio model is built based on GARCH model,and the model can capture the local fluctuations of the financial assets,which is helpful to control the risk proliferation. The smaller volatility of portfolio return and the higher Sharp ratio of the allocation are showed by simulating the financial data.
4. The spillover period concept and the spillover strength concept of the risk are raised,and the corresponding mathematical models are producted. At the same time,the empirical research reflect that Shanghai financial market impacts more deeply on the Shenzhen market,in contrary to,the Shenzhen market more weakly impacts Shanghai.And the 3 minute spillover period is reflected.The results are consistent to the fact.
5.The common factor extraction method of Statistical physics is used in the capital asset pricing in order that the revised CAPM are invented. The model is more capable than the original model in capital asset pricing.
These theoretical results were in five main sections of the paper, and, these studies were processed by following from the basis theory to the methods and the models, and ,last fact test ,so ,the metioned outcomes are scientific and practicality.
1.以统计物理学中的随机相关矩阵特征值概率密度为理论依据,构建了收益相关矩阵选取方法,从而解决了收益相关矩阵优选问题。实证检验显示,按由该方法所选取的收益相关矩阵配置资产可得到优质的有效前沿。
2.以多元统计学中的Wishart概率密度为理论依据,推导出相关系数的修正模型,该模型剔除了样本容量效应,使相关性度量更为准确可靠。实证结果显示,该模型具有较高的资产配置效率。
3.基于协同持续思想通过GARCH模型技术构建了动态投资组合模型,该模型可捕捉到金融资产收益的局部波动,达到控制风险扩散的目的。实证显示,按该模型配置资产可控制组合收益率在较小范围内波动,也可得较高夏普比。
4.提出风险溢出发生期及风险溢出强度两个概念,并构建了相应数学模型。同时,基于该模型进行了实证研究,结果显示,沪市影响深市的程度较深市影响沪市的程度大,且它们之间的风险溢出在大约3分钟之内完成,这一研究结果与实际吻合。
5.将统计物理学中的公因子提取法运用于资本资产定价方面,提出了CAPM修正模型。实证结果显示该模型较原模型具有较高的定价能力。
上述理论成果依次在论文五个主体章节中展开讨论,这些研究成果均遵循从理论依据到方法构建、模型提出,再到实证检验的研究思路,从而确保了研究工作的科学性和实用性。
It is most important step to study on the correlation and persistence of the financial capital return,especially,is most crucial work measuring accuratelly the correlation and persistence to explore the mechanism and operation of the capital market. To this end, by applying the theory of statistical physics and multiple-statistics and the model for financial measures to the practical problems of financia field, the achievements are as follows:
1. The method to discerning the best correlation matrix is obtainded by the random matrix eigenvalue probability density function in statistical physics solving the matrix optimization. Empirical tests show that the efficient frontier may be bettler by the method .
2. Based on Wishart probability distribution of multiple statistics, the revised model of the correlation coefficient is derived so that the sample pool doubt disappear and so the correlation coefficient becomes an accurate measure tool.
3. After considering the Co-persistence thought, the dynamic portfolio model is built based on GARCH model,and the model can capture the local fluctuations of the financial assets,which is helpful to control the risk proliferation. The smaller volatility of portfolio return and the higher Sharp ratio of the allocation are showed by simulating the financial data.
4. The spillover period concept and the spillover strength concept of the risk are raised,and the corresponding mathematical models are producted. At the same time,the empirical research reflect that Shanghai financial market impacts more deeply on the Shenzhen market,in contrary to,the Shenzhen market more weakly impacts Shanghai.And the 3 minute spillover period is reflected.The results are consistent to the fact.
5.The common factor extraction method of Statistical physics is used in the capital asset pricing in order that the revised CAPM are invented. The model is more capable than the original model in capital asset pricing.
These theoretical results were in five main sections of the paper, and, these studies were processed by following from the basis theory to the methods and the models, and ,last fact test ,so ,the metioned outcomes are scientific and practicality.
引文
[1] Markowitz H M.Portfolio selection[J].Joumal of Finance,1952,7:77-91.
[2] Sharpe W.Capital asset prices:a theory of market equilibrium under conditions of risk[J].Journal of Finance,1964,19: 425～442.
[3] Lintner J.The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets[J].Review of Economics and Statistics,1965,47:13～37.
[4] Mossin J.Equilibrium in a capital asset market[J].Econometrica,1966,34:768～783.
[5] Black F.Scholes M.The pricing of options and corporate liabilities[J]. Journal of Political Economy,1973,81(3):637～654.
[6] Fama E F.Efficient capital markets:a review of empifical work[J].Journal of Finance,1970,25:383～417.
[7] Ross S A.The arbitrage theory of capital asset pricing[J].Journal of Economic Theory,1976,13:341～360.
[8]朱书尚,李端,周迅宇,汪寿阳.论投资组合与金融优化[J].管理科学学报,2004 ,7(6):1～12.
[9]张卫国.现代投资组合理论—模型方法与应用.北京:科学出版社,2007.
[10] Young W,Trent R.Geometric mean approximations of individual securities and porffolio perfoamance[J].Journal of Financial and Quantitative Analisis,1969,2:179～488.
[11] Elton E J,Gruber M J.An algorithm for maximizating the geometric mean[J].Manage Sci,1974,3:483～488.
[12] Aditti F . Portfolio efficient analysis in three moment : the multiperiod case[J].Journal of finance,1975,3:797～809.
[13] Jean W H,Helms B R.Geometric mean approximations[J].Journal of Financial and Quantitative Analisis,1983,3:287～294.
[14] Brennan M J ,Schwartz E S.On the Geometric mean index a note[J].Journal of Financial and Quantitative Analisis,1985,1:119～122.
[15] Samuelson P.the fundamental appmximation theorem ofportfolio analysis in terms ofmeans variances and higher moments[J].Review of Economic Studies,l958,25:65～86.
[16] Konno H,Suzuki K.A mean variance skewness portfolio optimization model[J].Journal of Operation Research Society of Japan ,1995,38:173～187.
[17]许启发.高阶矩波动性建模及应用[J].数量经济技术经济研究,2006,12:135～145.
[18]许启发,张世英.多元条件高阶矩波动性建模[J].系统工程学报,2007,22(1):1～8.
[19]许启发,王艳明.基于小波多分辨分析的高阶矩CAPM[J].统计研究,2007,24(4):31～36.
[20]蒋翠侠,许启发,张世英.金融市场条件高阶矩风险与动态组合投资[J].中国管理科学,2007,15(1):27～33.
[21] Roy A D.Safety-first and the holding of assets[J].Econometrics,1952,20:431～449.
[22] Plye D,Turnovsky S.Safty-first and the expected utility maximization in mean-standard deviation portfolio analysis[J].Rev of Econ,1970,1:75～81.
[23]王春峰,屠新曙,历斌.效用函数意义下投资组合有效选择问题的研究[J].中国管理科,2002,10(2):15～19.
[24] Carlsson C,Fuller R,Majlender P.A possibilitic approach to selecting portfolios with highest utility score[J].Fuzzy Sets and Systems,2002,131:13～21.
[25] Zhang W G,Wang Y L.Portfolio selection possibilistic mean-variance model and possibilistic efficient frontier[J]Lecture Note in Computer Science,2005,3521:203～213.
[26] Huang X X . Fuzzy chance-constrained portfolio selection[J] . Applied Mathematics and Computation,2006,117:500～507.
[27] Huang C F.An application of calculated fuzzy risk[J].Information Science,2002,142:37～56.
[28] Mao J C T.Models of capital budgeting,E-V versus E-S[J].Journal of Financial and Quantitative Analysis,1970,5:657～675.
[29] Konno H,Yamazaki H.Mean-absolute deviation portfolio optimization model and its application to Tokyo stock market[J].Man-agement Science,1991,37:519～531.
[30] Fishbum P C.Mean-risk analysis with risk associated with below-target returns[J].American Economical Review,1977,67:l16～l26.
[31] Feinstein C D,Thapa M N.Notes:A reformation of a mean-absolute deviation portfolio optimization[J].Manage Sci,1993,39:1552～1553.
[32] Speranza M G . Linear programming models for portfolio optimization[J].Fiance,1993,14:107～123.
[33] Ouderri B N,Sullivan W G..A semi-variance model for incorporating riskinto capital investment analysis[J].Journal of Engineering Economist,1991,2:211～223.
[34] Green R C,Hollifield B.When will mean-variance efficient portfolio be well diversified?[J].Journal of Finance,1992,47:1785～1809.
[35] Ogrycrak W,Ruszczynski A.On stochastic dominance and mean-semideriation modelInterim Report IR-97-043[R].International Institu for Applied Systems Analysis,1997,Luxembourg.
[36] Cai X Q,Teo K L,Yang X Q,Zhou X Y.Portfolio optimization under a minimax rule[J].Management Science,2000,46:957～972.
[37] Tanaka H,Guo P,Turksen I B.Portfolio selection based on fuzzy probabilities and possibility distribution[J].Fuzzy Set and System,2000,111:387～397.
[38] Fhilippe J.Value at risk: the new benchmark for controlling market risk[M].Chicago:irwin professional publishing.1996.
[39] Artzner P,Delbaen F,Eber J M,Heath D.Coherence measures of risk[J].Mathematical Finance,1999,9:203～228.
[40] Pflug G.Some remarks on the value-at-risk and the conditional value-at-risk [A].S.Uryasev Ed.Probabilistic Constrained Optimization:Methodology and Applications[C].Dordrecht:Kluwer Academic Publishers,2000.
[41] Basak S,Shapiro A.Value-at-risk-based risk managementoptimal policies and asset prices[J] .The Review of Financial Studies,2001,14(2):25～31.
[42] Bogentoft E,Romeijn H E,Uryasev S.Asset/liability management for pension funds using CVaR constraints[J].Journal of RiskFinance,2001,3:57～71.
[43] Rockafelar R T , Uryasev S . Optimization of conditional Value-at-Risk [J].Journal of Risk,2000,2:2l～41.
[44] Rockafelar R T,Uryasev S.Conditional Value-at-Risk for general loss distributions[J].Journal of Banki and Finance,2002,26:1443～1471.
[45] Topaloglou N,Vladimirou H,Zenios S A.CVaR Models with selective hedging for international asset allocation[J].Journal of Banking and Finance,2002,26 :l535～l561.
[46] Castellacci G,Siclari M J.The practice of Delta-Gamma VaR:Implementing the quadratic portfolio model[J] . European Journal of Operational Research.2003,150:529～545.
[47] Arnott R D , Wanger W H . The measurement and control of trading cost[J].Financial Analysis Journa,l990,46(6):73～80.
[48] Patel N R,Subrahmanyam N.A simple algorithm for optimal portfolio selection with fixed transaction costs[J].Management Science,1982,28:303～314.
[49] Yishimoto A.The mean-variance approach to portfolio optimization subject totransaction cost[J].Journal of Operations Research Society of Japan,1996,39:99～117.
[50] Mao J,Essencials of portfolio diversification strategy[J].Journal of Finance,1970,25:1109～1121.
[51] Jacob N L,A limited-diversfication portfolio selection model for the small investor[J].Journal of Finance,1974,29:847～856.
[52] Morton A J,Pliska S.Optimal portfolio management with fixed transaction cost[J].Mathematics Finance,1995,4:337～356.
[53] Li Z F,Wang S Y,Deng X T.A linear programming algorithm for optimal portfolio selection with transaction cost[J].International Journal of System Science,2000,31(1):107～117.
[54] Pogue G A.An extension of the Markowitz portfolio selection model to include variable transaction,short sales,leverage policies and taxes[J].Journal of Finance,1970,25:1005～1028.
[55] Chen A H,Jen F C,Zionts S.The optimal portfolio revision policy[J].Journal of Bussiness,1971,44:51～61.
[56] Kamin J . Optimal portfolio revision with a proportional transactions costs[J].Management Science,1975,21:1263～1271.
[57] Davis M H,Norman A R.Portfolio selection with transaction costs[J].Math Oper Res,1990,15:676～713.
[58] Mulvey J M,Vladimirou H.Stochastic network programming for financial planning problem[J],Managemengt Science,1992,38:1642～1664.
[59] Dantzig G B,Infanger G.Multi-stage stochastic linear programs for portfolio optimization[J].Annals of Operations Research,1993 45:59～76.
[60] Atkinson C,Al-Ali B.On an investment-consumption model with transaction cost:an asymptotic analysis[J].Applied Mathematical Finance,1997,4:109～113.
[61] Elton E J,Gruber M J.On the optimality of some multiperiod portfolio selection criteria[J].Journal of Business,1974,47:231～243.
[62] Cox J,Chuang C F.Optimal consumption and portfolio polices when asset price follow a diffusion process[J].J Econ Theory,1989,49:33～83.
[63] Dumas B,Luciano E.An exact solution to a dynamic portfolio choice problem under transaction ccsts[J].Journal of Finance,1991,46 :577～595.
[64]唐小我,傅庚,曹长修.非负约束条件下组合证券投资决策方法研究系统工程[J].1994,6:23～29.
[65]杨德权,胡运权,刘鹏伟,不允许卖空时证券组合前沿的性质研究[J].预测,1997,176:46～49.
[66]于维生.组合证券投资的有效边界[J].数理统计与管理,1998,3:27～31.
[67]张京,马树才.非负约束条件下组合证券投资决策的二次规划计算方法[J]预测,1998,174:44～46.
[68]张卫国,聂赞坎.选择资产组合的EP-MV模型及算法[J]运筹学学报,2003,3:56～66.
[69] perold A F.Large-scale portfolio optimization[J].Management Science,1984,30:1143～1160.
[70] Konno H,Suzuki K.A fast algorithm for solving large scale mean-variance models by compact factorization of covariance matrices[J].Journal of Operation Search Society of Japan,1992,35:93～104.
[71] Kawadai N,Konno H.Solving large scale mean-variance model with dense non-factorable matrices[J].Journal of Operation Search Society of Japan,2001,44(3):251～260.
[72] Konno H,Shirakawa H.Equilibrium relations in a capital asset market a mean absolute deviation approach[J].Finance Engineering and the Japaness Market,1994,1:21～35.
[73] Konno H,Thach P T,Tuy H.Optimization on low rank nonconvex structure[M].Kluwer Academic Publishers,1997.
[74] Konno H,Suzuki T,Kobayashi D.A branch and bound algorithm for solving mean-risk-skewness model[J].Optimization Method and Software,1998,10:297～317.
[75] Konno H,Wijayanayake A.Portfolio optimization problem under concave transaction costs and minimal transaction unit constraint[J].Math Program,2001,89:233～250.
[76] Konno H,Wijayanayake A.Mean-absolute derivation portfolio optimization model under transaction costs[J]. Journal of Operation Search Society of Japan,1999,42:422～435.
[77] Konno H , Wijayanayake A . Portfolio optimization problem under D.C. transaction costs and minimal transaction unit constraint[J].Journal of Global Optimization,2002,22:137～154.
[78] Rollanf E.A tabu search method for constrained Real-Number search:application to portfolio selection[R].Technical report.Dept.of accounting management information systems.Ohio State University ,Colunbus U S A,1997.
[79] Schaerf A . Local search techniques for constrained portfolio selection problem[J]. Computers and Operation Research,2000,27:1271～1302.
[80] Chang T J,Mead N,Beaslay J,Sharaiha Y.Heuristics for cardinality constrained portfolio optimization[J].Computers and Operation Research,2000,27:1271～1302.
[81] Xia Y S,Liu B D,Wang S Y,Lai K K.Anew model for portfolio selection with order of expected returns[J].Computers and Operation Research,2000,27:409～422.
[82] Xia Y S,Wang S Y,Deng X T.A compromise solution to mutual funds portfolio selection with transaction costs[J] . Computers and Operation Research,2001,134:564～581.
[83] Gilli M,Kellezi E.The threshold accepting heuristic for index trackng.In Financial Engineering , E-commerce and supply chain . Kluwer Applied Optimization Series,2002,1～18.
[84] Crama Y,Schyns M.Simulated annealing for complex portfolio selection problem[J].European Journal of Operation Research,2003,546～571.
[85] Lean Y,Wang S Y,Lai K K.An integrated data preparation scheme for neural network data analysis[J] . IEEE Transaction on Knowledge and Data Engineering,2006,18:1～13.
[86] Tiryaki F,Ahlatcioglu M.Fuzzy stock selection using a new fuzzy ranking and weighting algorithm[J].Applied Mathematical and Computation,2005,170:144～157.
[87] ]Merton R C . Lifetime portfolio selection under uncertainty : The continuous-time case[J].Review of Economics and Statistics,1969,51:247～257.
[88] Breeden D T . Consumption , production , inflation , and interes :tpsynthesls[J].Rev Econ Stat,1969,51:247～255.
[89] Harrison M,Kreps D.Martingales and arbitrage in multiperiod securities markets[J].J Econ Theory,1979,2:381～408.
[90] Harrison M,Pliska S.Martingales and stochastic intergrals in theory of continuous trading[J].Stochastic Precess App,1981,11:215～260.
[91] Karatzas I.Optimization problems in continuous trading[J].SIAM J.On Contral and Optimization,1989,27:1221～1259.
[92] Duffie D,Sun T.Transaction costs and portfolio choice in a discrete continuous time seting[J].J Econ Dynamic Contro,l990,14:35～51.
[93] Korn R,Trautmann S.Continuous-time portfolio optimization under terminal weath constraints[J].ZOR,1995,42:69～93.
[94] Korn R . Value preserving portfolio strategies in continuous-time models[J].Mathematical Methods of Operation Research,1997,45:1～43.
[95] Mossin J.Optimal multiperiod portfolio policies[J].Journal of Business,1968,41:215～229.
[96] Samuelson P . Lifetime portfolio selection by dynamic stochastic programming[J]. Review of Economics and Statistics,1969:50:239-246.
[97] Merton R C.Lifetime portfolio selection under uncertaintythe continuous time case[J].Rev Econ Stat,1969,51:247～255.
[98] Merton R C.Continuous-Time Finance[M].Cambridge,MA:Basil Blackwel,1990.
[99] Fama E F . Multiperiod consumption-investment decisions[J] . American Economic Review,1970,60:163～174.
[100] Ziemba W T,Mulvey J M.Worldwide Asset and Liability Modelling [M].Cambridge:Cambridge University Press,1998.
[101] Li D , Ng W L . Optimal dynamic portfolio selection : Multi-period mean-variance formulation [J].Mathematical Finance,2000, 10: 387～406.
[102] Zhou X Y,Li D.Continuous time mean-variance portfolio selection:A stochastic LQ framework[J].Applied Mathematics andOptimization,2000,42:19～33.
[103] Lim A E B,Zhou X Y.Mean-variance portfolio selection with random parameters[J].Mathematics of Operations Research,2002,27:101～120.
[104] Li X,Zhou X Y,Lim A E B.Dynamic mean-variance portfolio selection with no-shorting constraints[J].SIAM Joumal on Control and Optimization,2002,40:1540～1555.
[105] Zhou X Y,Yin G.Markowitz’s mean-variance portfolio selection with regime switching : A continuous-time model[J] . SIAM Journal on Control and Optimization,2003,42:1466～1482.
[106] Watada J . Fuzzy portfolio selection and its applications to decision making[J].Tatra Mountains Mathematical Publication,1997,13:219～248.
[107] Ramaswamy S.Portfolio selection using fuzzy decision theory[R].Working paper of Bank fou International Settlements,1998.No59.
[108] Dubois D,Prade H.The mean value of a fuzzy number[J].Fuzzy and Systems,1987,24:279～300.
[109] Tanaka H,Guo P.Portfolio selection based on upper and lower exponential possibility distributions[J].Eropean Journal of Operational Research,1999,114:115～126.
[110] Zadeh L A . Toward a generalized theory of uncertainty ( GTU ) -an outline[J].Information Sciences,2005,172:1～40.
[111] Parra M A,Terol A B.A fuzzy goal programming approach to portfolio selection[J].Eropean Journal of Operational Research,2001,133:287～297.
[112] Lin C,Tan B,Hsieh P J.Application of the fuzzy weighted average in strategicportfolio management [J].Decision Science,2005,36:489～511.
[113] Fang Y,Lai K K,Wang S Y.Portfolio rebalancing model with transaction costs based on fuzzy decision theory[J].Eropean Journal of Operational Research,2006,175:879～893.
[114] Lai K K,Wang S Y,Xu J P,Zhu S S,Fang Y.A class of linear interval programming problems and its application to portfolio selection[J].IEEE Transactions on Fuzzy Systems,2002,10:698～704.
[115] Giove S,Funari S,Nardelli C.An interval portfolio selection promblems based on regret fuction[J].Eropean Journal of Operational Research,2006,176(1):208～218.
[116] Zhang W G , Nie Z K . On admissible efficient portfolio selection problem[J].Application Mathematical and Computation,2004,159(2):357～371.
[117] Hakansson N.Opitimal investment and consumption strategies under risk for a class of utility function[J].Econometrica,1970,38:587～607.
[118] Long J B.Stockinflationand the term structure of interest rates[J].J Financ Econ,1974,2:131～170.
[119] Rubinstein M.The valuation of uncertain income streams and the pricing of options[J].Bull J Econ Manage Sci,1976,7:407～425.
[120] Emmer S , Kluppelberg C , Korn R . Optimal portfolios with bounded capital-at-risk[J].Mathematical Finance,2001,11:365～384.
[121]张世英,李汉东,樊智.金融风险的持续性及其规避策略[J].系统工程理论与实践,2002,22(5):31～36.
[122]李汉东,张世英.BEKK模型的协同持续性研究[J].系统工程学报,2001,16(3):181～186.
[123]李汉东,张世英.随机波动模型的持续性和协同持续性研究[J].系统工程学报,2002,17(4):289～295.
[124]杜子平,张世英.向量GATCH过程协同持续性研究[J].系统工程学报,2003,18(5):385～390.
[125]刘丹红,徐正国,张世英.向量GARCH模型的非线性协同持续[J].系统工程,2004,22(6):33～38.
[126]刘丹红,徐正国,张世英.上海股市投资组合的非线性协同研究[J].系统工程理论方法应用,2005,14(3):275～279.
[127]蒋翠侠.动态金融风险测度及管理研究[D].天津大学,2008.
[128] Schwert G .W , Seguin P J . Heteroskedasticity in Stock Returns[J].Journal of Finance,1990,25:1129～1155.
[129] Bollerslev T.Modeling the coherence in short-run nominal Exchange rates:amultivariate GARCH approach[J].Review of Economics and Statistics,1990,72 :498～505.
[130] Hamao Y,Masulis R W,Ng V.Correlations in price Changes and volatility across international stock markets[J].Review of Financial Studies,1990,24:2 41～256.
[131] Scheicher M.The comovements of stock markets in Hungary,Poland and the Czech Republic[J].International Journal of Finance and Economics,2001,l6:27～39.
[132] Theodossiou P,Lee U.Mean and volatility spillovers across major national stock markets:further empirical evidence[J].Journal of Financial Research,1993,16:337～350.
[133] Bae K,Karolyi G.Good news,bad news and international spillovers of stock return volatility between Japan and the U S,Pacific Basin[J].Finance Journal,1994,2:405～438.
[134] Engle R,Kroner K.Multivariate Simultaneous GARCH[J].Econometric Theory,1995,11:122～150.
[135] Koutmos G,Booth G.A symmetric volatility transmission in international stock markets[J].Journal of International Money and Finance,1995,14:7 47～762.
[136] Booth G,Martikainen T and Yiuman T.Price and Volatility Spillovers in Scandinavian stock markets[J].Journal of Banking and Finance,1997,21:811～823.
[137] Engle R F.Dynamic conditional correlation:a simple class of multivariate generalized autoregressive conditional heteroskedasticity models[J].Journal of Business and Economic Statistics,2002,20:339～350.
[138]赵留彦,王一鸣.A,B股之间的信息流动与波动溢出.金融研究[J].2003,280(10):37～52.
[139]谷耀,陆丽娜.沪,深,港股市信息溢出效应与动态相关性[J].数量经济技术经济研究,2006,8:142～151.
[140]方毅,张屹山.国内外金属期货市场“风险传染”的实证研究[J].金融研究,2007,323(5):133～146.
[141]赵华.人民币汇率与利率之间的价格和波动溢出效应研究[J].金融研究,,2007,321(3):41～49.
[142]吴文锋,刘太阳,吴冲锋.上海与伦敦期铜市场之间的波动溢出效应研究[J].系统工程理论方法应用,2007,3:111～115.
[143] Ripley D M.Systematic elements in the linkage of national stock market indices[J].Review of Economics and Statistics,1973,55:356～361.
[144] Panton V,Parker and Joy.Comovement of international equity markets:a taxonomic approach[J].Journal of Financial and Quantative Analysis,1976,415～432.
[145] Engle R F , Granger C W J . Co-integration and error correction: representation,estimation and testing[J].Econometrica,1987,55(2):251～276.
[146] Eun C,Shim S.International transmission of stock price movements[J].Journal of Financial and Quantitative Analysis,1989,24:241～256.
[147] Jeon B and Von Furstenberg G. M.Growing international co-movements in stock price indexes[J].Quarterly Review of Economics and Business,1990,30:15～30.
[148] Tay,S P,Zhu,Z.Correlations in returns and volatilities in Pacific-Rim stock markets[J].Open Economies Review,2000,11:27～47.
[149] Zhang R F, Zou Q W, Chen J. Common volatility spillover analysis and empirical study on the financial market based on the independent components[C]. Proceedings of 2006 International conference on Management Science & Engineering ,2006:1714～1718.(EI收录: 9264009)
[150]张瑞锋,张世英.唐勇.金融市场波动溢出分析及实证研究[J].中国管理科学,2006,14(5):14～22.
[151] Zhang R F,Zou Q W, Zhang S Y.Volatility spillover analysis and empirical study on the financial market based on copula theory [C].Proceedings of 2007 International conference on Management Science & Engineering ,2007:1874～1881.(ISTP收录)
[152] Black F.Capital market equilibrium with restricted borrowing[J].Joumal of Business,1972,45:444～454.
[153] Mayers D.Non-marketable assets and capital market equilibrium under uncertainty[C].Studies in the Theory of Capital Markets,Praeger Publishers,1972.
[154] Merton,Robert C.Continuous-time Finance[M].Blackwell Publishers,1990.
[155] Breeden,Douglas T.An intertemporal asset pricing model with stochastic consumption and investment opportunities[J].Journal of Financial Economics,1979,7:265～296.
[156] Roll R,Ross S A.An empirical investigation of the arbitrage pricing theory[J],Journal of Finance,1980,35:1073～l103.
[157] Fama E F,French K R.The cross-section of expected stock returns[J].Journal of Finance,1992,4:427～465.
[158]陈小悦,孙爱军.CAPM在中国股市的有效性检验[J].北京大学学报(哲学社会科学版),2000(4):37～42.
[159]李和金,李湛.上海股票市场资本资产定价模型实证检验[J].预测,2000,5:75～78.
[160]陈浪南,屈文洲.资本资产定价模型的实证研究[J].经济研究,2000,4:26～34.
[161] Roll R.A critique of the asset pricing theory’tests:part 1.JournaI of Financilal Economics.1977,4:129～176.
[162] Dyson F.Statistical theory of the energy levels of complex systems i–iii[J].Math. Phys,1962,3:140～175.
[163] Mehta M,Dyson F.Statistical theory of the energy levels of complex systems iv[J].Math. Phys,1963,4(5):713～719.
[164] Dyson F,Mehta M.Statistical theory of the energy levels of complex systems v[J].Math Phys,1963,4(5):701～712.
[165] Plerou V,Gopikrishnan P,Rosenow B,Amaral L,Stanley H E.Universal and non-universal properties of cross-correlations in financial time series[J].Phys Rev Lett,1999,83(7):1471～1474.
[166] Plerou V,Gopikrishnan P,Rosenow B,Amaral L,Stanley H E.Econophysics:financial time series from a statistical point of view[J].Physica A, 2000,279:443～456.
[167] Plerou V,Gopikrishnan P,Rosenow B,Amaral L,Stanley H E.A random matrix theory approach to financial cross-correlations[J],Physica A ,2000,287:374～382.
[168] Ghashghaie S,Breymann W,Peinke J,Taikner P,Dodge Y.Turbulent cascades in foreign exchange market[J].Nature,1996,381:767～770.
[169] Mantegna R N,Stanley H E.Turbulence and financial markets[J].Nature,1996,383:587～588.
[170] Mantegna R N,Stanley H E.Stock market dynamics and turbulence:paralell analysis of fluctuation phenomena[J].Physica A,1997,239:255～266.
[171] Potter M , Cont R , Bouch J P . Financail market as adaptive ecosystem[J].Europhys Lett,1998,41:239～242.
[172] Farmer J D.Market force,ecology and evolution[J]Adaporg preprint server 981,2005.
[173] Plerou V,Gopikrishnan P,Rosenow B,Amaral L,Guhr T,Stanley H E . Collective behaviour of stock price movements : a random matrix approach[J].Physica A,2001,299:175～180.
[174] BouyéE,Durrleman V,Nikeghbali A,et al.Copula:an open fields for risk management.Working Paper of Financial Econometrics Research Centre,City University Business School,London,2001.
[175] Alexander C O . Volatility and correlation : methods , models and applications[M].Risk Management and Analysis: Measuring and Modeling Financial Risk(C O Alexander,Ed)Wiley.
[176] Hamao Y,Masulis R W,Ng V K. Correlation in price changes and volatility across international stock markets[J].Review of Financial Studies, 1990,2(3):281～307.
[177] Sola M,Spagnolo F,Spagnolo N.A test for volatility spillovers[J].Economics Letters,2002,76:77～84.
[178]王海燕,杨方廷,刘鲁.标准化系数与偏相关系数的比较与应用[J].数量经济技术经济研究,2006,9:150～155.
[179]刘建华,赵晓波,卢红梅.多货币资产管理风险度量[J].上海金融,2004,7:38～41.
[180]陈东一,傅绍文.改革以来我国物价波动实证分析[J].山西财经大学学报,2003,25(4):35～37.
[181]陈华友.基于相关系数的优性组合预测模型研究[J].系统工程学报,2006,21(4):353～360.
[182]王政.全球近50年气温波动分析[J].数理统计与管理,2004,23(4):1～6.
[183] Anderson T W.Introduction to Multivariate Statistical Analysis(2d ed),NewYork:John Wily,1984.
[184] Bollerslev T . Generalized autoregressive conditional heteroskedasticity[J]. Journal of Economics,1986,,31:307～327.
[185] Engle R F.Autoregressive heteroskedasticity with estimation of the variance of U K inflation[J].Econometrica,1982,50:987～1008.
[186] Engle R F , Bollerslev T . Modeling the persistence of conditional variances[J].Econometric Review,1986,5:1～50.
[187] Nelson D B . Conditional heteroskedasticity in asset returns : a new approach[J].Econometrica,1991,59:347～370.
[188] Baillie R T,Bollerslev T,Mikkelsen H O.Fractionally integrated generalized autoregressive conditional heteroskedasticity[J].Journal of Econometrics,1996,74:3～30.
[189] Bollerslev T,Engle R F,Wooldridge J.A capital asset pricing model with time varying covariances[J].Journal of Political Economy,1988,96:116～131.
[190]张世英,柯珂.分整增广GARCH-M模型[J].系统工程学报,2003,18(1):16～24.
[191] Bollerslev T , Engle R F . Common persistence in conditional Variances[J].Economitrica,1993,61(1):167～186.
[192] Ding Zh X,Granger C W J.Modeling volatility Persistence of speculative returns:a new approach[J].Journal of Econometrics,1996,73:185～215.
[193] Li Han-dong, Zhang Shi-ying.Common persistence and error-correctionmodel in conditional variance[J].Journal of System Science and System Engineering, 2001,10(3):257～264.
[194]徐绪松,马莉莉,陈彦斌.我国上海股票市场GARCH效应实证研究[J].武汉大学学报(理学版),2002,48(3):293～296.
[195]皮天雷.我国沪市波动聚集性GARCH效应的实证研究[J].管理科学,2003,16(6):31～35.
[196] Anderson T G,Bollerslev T,Diebold F,Labys P.Exchange Rate Returns Standardized by Realized Volatility are (nearly)Gaussian[J].Multinational Finance Journa1,2000,(4):159～179.
[197]郭名媛,张世英.赋权已实现波动及其长记忆性,最优频率选择[J].系统工程学报,2006,21(6):568～573.
[198]唐勇,张世英.已实现波动和已实现极差波动的比较研究[J].系统工程学报,2007,22(4):437～442.
[199]韩清,刘永刚.序列相关的微观结构噪声估计[J].数量经济技术经济研究,2007,4:92～102.
[200] Fama,Eugene F.Efficient capital markets:a review of theory and empirical work [J].Journal of Finance 1970,25 (2):383～417.
[201] Plerou V,Gopikrishnan P,Rosenow B,Amaral L,Guhr T,Stanley H E. A random matrix approach to cross-correlations in financial data[J].Phys Rev E,2002,65(6):1～18.
[202] Colon T,Ruskin H J,Crane M.Random matrix theory and fund of funds portfolio optimization[J].Physica A,2007,382:565～576.
[203] Rosario N Mantegna,H Eugene Stanley,封建强(译),匡宏波(译).An introductong to econophysics[M].北京:中国人民大学出版社,2005
[2] Sharpe W.Capital asset prices:a theory of market equilibrium under conditions of risk[J].Journal of Finance,1964,19: 425～442.
[3] Lintner J.The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets[J].Review of Economics and Statistics,1965,47:13～37.
[4] Mossin J.Equilibrium in a capital asset market[J].Econometrica,1966,34:768～783.
[5] Black F.Scholes M.The pricing of options and corporate liabilities[J]. Journal of Political Economy,1973,81(3):637～654.
[6] Fama E F.Efficient capital markets:a review of empifical work[J].Journal of Finance,1970,25:383～417.
[7] Ross S A.The arbitrage theory of capital asset pricing[J].Journal of Economic Theory,1976,13:341～360.
[8]朱书尚,李端,周迅宇,汪寿阳.论投资组合与金融优化[J].管理科学学报,2004 ,7(6):1～12.
[9]张卫国.现代投资组合理论—模型方法与应用.北京:科学出版社,2007.
[10] Young W,Trent R.Geometric mean approximations of individual securities and porffolio perfoamance[J].Journal of Financial and Quantitative Analisis,1969,2:179～488.
[11] Elton E J,Gruber M J.An algorithm for maximizating the geometric mean[J].Manage Sci,1974,3:483～488.
[12] Aditti F . Portfolio efficient analysis in three moment : the multiperiod case[J].Journal of finance,1975,3:797～809.
[13] Jean W H,Helms B R.Geometric mean approximations[J].Journal of Financial and Quantitative Analisis,1983,3:287～294.
[14] Brennan M J ,Schwartz E S.On the Geometric mean index a note[J].Journal of Financial and Quantitative Analisis,1985,1:119～122.
[15] Samuelson P.the fundamental appmximation theorem ofportfolio analysis in terms ofmeans variances and higher moments[J].Review of Economic Studies,l958,25:65～86.
[16] Konno H,Suzuki K.A mean variance skewness portfolio optimization model[J].Journal of Operation Research Society of Japan ,1995,38:173～187.
[17]许启发.高阶矩波动性建模及应用[J].数量经济技术经济研究,2006,12:135～145.
[18]许启发,张世英.多元条件高阶矩波动性建模[J].系统工程学报,2007,22(1):1～8.
[19]许启发,王艳明.基于小波多分辨分析的高阶矩CAPM[J].统计研究,2007,24(4):31～36.
[20]蒋翠侠,许启发,张世英.金融市场条件高阶矩风险与动态组合投资[J].中国管理科学,2007,15(1):27～33.
[21] Roy A D.Safety-first and the holding of assets[J].Econometrics,1952,20:431～449.
[22] Plye D,Turnovsky S.Safty-first and the expected utility maximization in mean-standard deviation portfolio analysis[J].Rev of Econ,1970,1:75～81.
[23]王春峰,屠新曙,历斌.效用函数意义下投资组合有效选择问题的研究[J].中国管理科,2002,10(2):15～19.
[24] Carlsson C,Fuller R,Majlender P.A possibilitic approach to selecting portfolios with highest utility score[J].Fuzzy Sets and Systems,2002,131:13～21.
[25] Zhang W G,Wang Y L.Portfolio selection possibilistic mean-variance model and possibilistic efficient frontier[J]Lecture Note in Computer Science,2005,3521:203～213.
[26] Huang X X . Fuzzy chance-constrained portfolio selection[J] . Applied Mathematics and Computation,2006,117:500～507.
[27] Huang C F.An application of calculated fuzzy risk[J].Information Science,2002,142:37～56.
[28] Mao J C T.Models of capital budgeting,E-V versus E-S[J].Journal of Financial and Quantitative Analysis,1970,5:657～675.
[29] Konno H,Yamazaki H.Mean-absolute deviation portfolio optimization model and its application to Tokyo stock market[J].Man-agement Science,1991,37:519～531.
[30] Fishbum P C.Mean-risk analysis with risk associated with below-target returns[J].American Economical Review,1977,67:l16～l26.
[31] Feinstein C D,Thapa M N.Notes:A reformation of a mean-absolute deviation portfolio optimization[J].Manage Sci,1993,39:1552～1553.
[32] Speranza M G . Linear programming models for portfolio optimization[J].Fiance,1993,14:107～123.
[33] Ouderri B N,Sullivan W G..A semi-variance model for incorporating riskinto capital investment analysis[J].Journal of Engineering Economist,1991,2:211～223.
[34] Green R C,Hollifield B.When will mean-variance efficient portfolio be well diversified?[J].Journal of Finance,1992,47:1785～1809.
[35] Ogrycrak W,Ruszczynski A.On stochastic dominance and mean-semideriation modelInterim Report IR-97-043[R].International Institu for Applied Systems Analysis,1997,Luxembourg.
[36] Cai X Q,Teo K L,Yang X Q,Zhou X Y.Portfolio optimization under a minimax rule[J].Management Science,2000,46:957～972.
[37] Tanaka H,Guo P,Turksen I B.Portfolio selection based on fuzzy probabilities and possibility distribution[J].Fuzzy Set and System,2000,111:387～397.
[38] Fhilippe J.Value at risk: the new benchmark for controlling market risk[M].Chicago:irwin professional publishing.1996.
[39] Artzner P,Delbaen F,Eber J M,Heath D.Coherence measures of risk[J].Mathematical Finance,1999,9:203～228.
[40] Pflug G.Some remarks on the value-at-risk and the conditional value-at-risk [A].S.Uryasev Ed.Probabilistic Constrained Optimization:Methodology and Applications[C].Dordrecht:Kluwer Academic Publishers,2000.
[41] Basak S,Shapiro A.Value-at-risk-based risk managementoptimal policies and asset prices[J] .The Review of Financial Studies,2001,14(2):25～31.
[42] Bogentoft E,Romeijn H E,Uryasev S.Asset/liability management for pension funds using CVaR constraints[J].Journal of RiskFinance,2001,3:57～71.
[43] Rockafelar R T , Uryasev S . Optimization of conditional Value-at-Risk [J].Journal of Risk,2000,2:2l～41.
[44] Rockafelar R T,Uryasev S.Conditional Value-at-Risk for general loss distributions[J].Journal of Banki and Finance,2002,26:1443～1471.
[45] Topaloglou N,Vladimirou H,Zenios S A.CVaR Models with selective hedging for international asset allocation[J].Journal of Banking and Finance,2002,26 :l535～l561.
[46] Castellacci G,Siclari M J.The practice of Delta-Gamma VaR:Implementing the quadratic portfolio model[J] . European Journal of Operational Research.2003,150:529～545.
[47] Arnott R D , Wanger W H . The measurement and control of trading cost[J].Financial Analysis Journa,l990,46(6):73～80.
[48] Patel N R,Subrahmanyam N.A simple algorithm for optimal portfolio selection with fixed transaction costs[J].Management Science,1982,28:303～314.
[49] Yishimoto A.The mean-variance approach to portfolio optimization subject totransaction cost[J].Journal of Operations Research Society of Japan,1996,39:99～117.
[50] Mao J,Essencials of portfolio diversification strategy[J].Journal of Finance,1970,25:1109～1121.
[51] Jacob N L,A limited-diversfication portfolio selection model for the small investor[J].Journal of Finance,1974,29:847～856.
[52] Morton A J,Pliska S.Optimal portfolio management with fixed transaction cost[J].Mathematics Finance,1995,4:337～356.
[53] Li Z F,Wang S Y,Deng X T.A linear programming algorithm for optimal portfolio selection with transaction cost[J].International Journal of System Science,2000,31(1):107～117.
[54] Pogue G A.An extension of the Markowitz portfolio selection model to include variable transaction,short sales,leverage policies and taxes[J].Journal of Finance,1970,25:1005～1028.
[55] Chen A H,Jen F C,Zionts S.The optimal portfolio revision policy[J].Journal of Bussiness,1971,44:51～61.
[56] Kamin J . Optimal portfolio revision with a proportional transactions costs[J].Management Science,1975,21:1263～1271.
[57] Davis M H,Norman A R.Portfolio selection with transaction costs[J].Math Oper Res,1990,15:676～713.
[58] Mulvey J M,Vladimirou H.Stochastic network programming for financial planning problem[J],Managemengt Science,1992,38:1642～1664.
[59] Dantzig G B,Infanger G.Multi-stage stochastic linear programs for portfolio optimization[J].Annals of Operations Research,1993 45:59～76.
[60] Atkinson C,Al-Ali B.On an investment-consumption model with transaction cost:an asymptotic analysis[J].Applied Mathematical Finance,1997,4:109～113.
[61] Elton E J,Gruber M J.On the optimality of some multiperiod portfolio selection criteria[J].Journal of Business,1974,47:231～243.
[62] Cox J,Chuang C F.Optimal consumption and portfolio polices when asset price follow a diffusion process[J].J Econ Theory,1989,49:33～83.
[63] Dumas B,Luciano E.An exact solution to a dynamic portfolio choice problem under transaction ccsts[J].Journal of Finance,1991,46 :577～595.
[64]唐小我,傅庚,曹长修.非负约束条件下组合证券投资决策方法研究系统工程[J].1994,6:23～29.
[65]杨德权,胡运权,刘鹏伟,不允许卖空时证券组合前沿的性质研究[J].预测,1997,176:46～49.
[66]于维生.组合证券投资的有效边界[J].数理统计与管理,1998,3:27～31.
[67]张京,马树才.非负约束条件下组合证券投资决策的二次规划计算方法[J]预测,1998,174:44～46.
[68]张卫国,聂赞坎.选择资产组合的EP-MV模型及算法[J]运筹学学报,2003,3:56～66.
[69] perold A F.Large-scale portfolio optimization[J].Management Science,1984,30:1143～1160.
[70] Konno H,Suzuki K.A fast algorithm for solving large scale mean-variance models by compact factorization of covariance matrices[J].Journal of Operation Search Society of Japan,1992,35:93～104.
[71] Kawadai N,Konno H.Solving large scale mean-variance model with dense non-factorable matrices[J].Journal of Operation Search Society of Japan,2001,44(3):251～260.
[72] Konno H,Shirakawa H.Equilibrium relations in a capital asset market a mean absolute deviation approach[J].Finance Engineering and the Japaness Market,1994,1:21～35.
[73] Konno H,Thach P T,Tuy H.Optimization on low rank nonconvex structure[M].Kluwer Academic Publishers,1997.
[74] Konno H,Suzuki T,Kobayashi D.A branch and bound algorithm for solving mean-risk-skewness model[J].Optimization Method and Software,1998,10:297～317.
[75] Konno H,Wijayanayake A.Portfolio optimization problem under concave transaction costs and minimal transaction unit constraint[J].Math Program,2001,89:233～250.
[76] Konno H,Wijayanayake A.Mean-absolute derivation portfolio optimization model under transaction costs[J]. Journal of Operation Search Society of Japan,1999,42:422～435.
[77] Konno H , Wijayanayake A . Portfolio optimization problem under D.C. transaction costs and minimal transaction unit constraint[J].Journal of Global Optimization,2002,22:137～154.
[78] Rollanf E.A tabu search method for constrained Real-Number search:application to portfolio selection[R].Technical report.Dept.of accounting management information systems.Ohio State University ,Colunbus U S A,1997.
[79] Schaerf A . Local search techniques for constrained portfolio selection problem[J]. Computers and Operation Research,2000,27:1271～1302.
[80] Chang T J,Mead N,Beaslay J,Sharaiha Y.Heuristics for cardinality constrained portfolio optimization[J].Computers and Operation Research,2000,27:1271～1302.
[81] Xia Y S,Liu B D,Wang S Y,Lai K K.Anew model for portfolio selection with order of expected returns[J].Computers and Operation Research,2000,27:409～422.
[82] Xia Y S,Wang S Y,Deng X T.A compromise solution to mutual funds portfolio selection with transaction costs[J] . Computers and Operation Research,2001,134:564～581.
[83] Gilli M,Kellezi E.The threshold accepting heuristic for index trackng.In Financial Engineering , E-commerce and supply chain . Kluwer Applied Optimization Series,2002,1～18.
[84] Crama Y,Schyns M.Simulated annealing for complex portfolio selection problem[J].European Journal of Operation Research,2003,546～571.
[85] Lean Y,Wang S Y,Lai K K.An integrated data preparation scheme for neural network data analysis[J] . IEEE Transaction on Knowledge and Data Engineering,2006,18:1～13.
[86] Tiryaki F,Ahlatcioglu M.Fuzzy stock selection using a new fuzzy ranking and weighting algorithm[J].Applied Mathematical and Computation,2005,170:144～157.
[87] ]Merton R C . Lifetime portfolio selection under uncertainty : The continuous-time case[J].Review of Economics and Statistics,1969,51:247～257.
[88] Breeden D T . Consumption , production , inflation , and interes :tpsynthesls[J].Rev Econ Stat,1969,51:247～255.
[89] Harrison M,Kreps D.Martingales and arbitrage in multiperiod securities markets[J].J Econ Theory,1979,2:381～408.
[90] Harrison M,Pliska S.Martingales and stochastic intergrals in theory of continuous trading[J].Stochastic Precess App,1981,11:215～260.
[91] Karatzas I.Optimization problems in continuous trading[J].SIAM J.On Contral and Optimization,1989,27:1221～1259.
[92] Duffie D,Sun T.Transaction costs and portfolio choice in a discrete continuous time seting[J].J Econ Dynamic Contro,l990,14:35～51.
[93] Korn R,Trautmann S.Continuous-time portfolio optimization under terminal weath constraints[J].ZOR,1995,42:69～93.
[94] Korn R . Value preserving portfolio strategies in continuous-time models[J].Mathematical Methods of Operation Research,1997,45:1～43.
[95] Mossin J.Optimal multiperiod portfolio policies[J].Journal of Business,1968,41:215～229.
[96] Samuelson P . Lifetime portfolio selection by dynamic stochastic programming[J]. Review of Economics and Statistics,1969:50:239-246.
[97] Merton R C.Lifetime portfolio selection under uncertaintythe continuous time case[J].Rev Econ Stat,1969,51:247～255.
[98] Merton R C.Continuous-Time Finance[M].Cambridge,MA:Basil Blackwel,1990.
[99] Fama E F . Multiperiod consumption-investment decisions[J] . American Economic Review,1970,60:163～174.
[100] Ziemba W T,Mulvey J M.Worldwide Asset and Liability Modelling [M].Cambridge:Cambridge University Press,1998.
[101] Li D , Ng W L . Optimal dynamic portfolio selection : Multi-period mean-variance formulation [J].Mathematical Finance,2000, 10: 387～406.
[102] Zhou X Y,Li D.Continuous time mean-variance portfolio selection:A stochastic LQ framework[J].Applied Mathematics andOptimization,2000,42:19～33.
[103] Lim A E B,Zhou X Y.Mean-variance portfolio selection with random parameters[J].Mathematics of Operations Research,2002,27:101～120.
[104] Li X,Zhou X Y,Lim A E B.Dynamic mean-variance portfolio selection with no-shorting constraints[J].SIAM Joumal on Control and Optimization,2002,40:1540～1555.
[105] Zhou X Y,Yin G.Markowitz’s mean-variance portfolio selection with regime switching : A continuous-time model[J] . SIAM Journal on Control and Optimization,2003,42:1466～1482.
[106] Watada J . Fuzzy portfolio selection and its applications to decision making[J].Tatra Mountains Mathematical Publication,1997,13:219～248.
[107] Ramaswamy S.Portfolio selection using fuzzy decision theory[R].Working paper of Bank fou International Settlements,1998.No59.
[108] Dubois D,Prade H.The mean value of a fuzzy number[J].Fuzzy and Systems,1987,24:279～300.
[109] Tanaka H,Guo P.Portfolio selection based on upper and lower exponential possibility distributions[J].Eropean Journal of Operational Research,1999,114:115～126.
[110] Zadeh L A . Toward a generalized theory of uncertainty ( GTU ) -an outline[J].Information Sciences,2005,172:1～40.
[111] Parra M A,Terol A B.A fuzzy goal programming approach to portfolio selection[J].Eropean Journal of Operational Research,2001,133:287～297.
[112] Lin C,Tan B,Hsieh P J.Application of the fuzzy weighted average in strategicportfolio management [J].Decision Science,2005,36:489～511.
[113] Fang Y,Lai K K,Wang S Y.Portfolio rebalancing model with transaction costs based on fuzzy decision theory[J].Eropean Journal of Operational Research,2006,175:879～893.
[114] Lai K K,Wang S Y,Xu J P,Zhu S S,Fang Y.A class of linear interval programming problems and its application to portfolio selection[J].IEEE Transactions on Fuzzy Systems,2002,10:698～704.
[115] Giove S,Funari S,Nardelli C.An interval portfolio selection promblems based on regret fuction[J].Eropean Journal of Operational Research,2006,176(1):208～218.
[116] Zhang W G , Nie Z K . On admissible efficient portfolio selection problem[J].Application Mathematical and Computation,2004,159(2):357～371.
[117] Hakansson N.Opitimal investment and consumption strategies under risk for a class of utility function[J].Econometrica,1970,38:587～607.
[118] Long J B.Stockinflationand the term structure of interest rates[J].J Financ Econ,1974,2:131～170.
[119] Rubinstein M.The valuation of uncertain income streams and the pricing of options[J].Bull J Econ Manage Sci,1976,7:407～425.
[120] Emmer S , Kluppelberg C , Korn R . Optimal portfolios with bounded capital-at-risk[J].Mathematical Finance,2001,11:365～384.
[121]张世英,李汉东,樊智.金融风险的持续性及其规避策略[J].系统工程理论与实践,2002,22(5):31～36.
[122]李汉东,张世英.BEKK模型的协同持续性研究[J].系统工程学报,2001,16(3):181～186.
[123]李汉东,张世英.随机波动模型的持续性和协同持续性研究[J].系统工程学报,2002,17(4):289～295.
[124]杜子平,张世英.向量GATCH过程协同持续性研究[J].系统工程学报,2003,18(5):385～390.
[125]刘丹红,徐正国,张世英.向量GARCH模型的非线性协同持续[J].系统工程,2004,22(6):33～38.
[126]刘丹红,徐正国,张世英.上海股市投资组合的非线性协同研究[J].系统工程理论方法应用,2005,14(3):275～279.
[127]蒋翠侠.动态金融风险测度及管理研究[D].天津大学,2008.
[128] Schwert G .W , Seguin P J . Heteroskedasticity in Stock Returns[J].Journal of Finance,1990,25:1129～1155.
[129] Bollerslev T.Modeling the coherence in short-run nominal Exchange rates:amultivariate GARCH approach[J].Review of Economics and Statistics,1990,72 :498～505.
[130] Hamao Y,Masulis R W,Ng V.Correlations in price Changes and volatility across international stock markets[J].Review of Financial Studies,1990,24:2 41～256.
[131] Scheicher M.The comovements of stock markets in Hungary,Poland and the Czech Republic[J].International Journal of Finance and Economics,2001,l6:27～39.
[132] Theodossiou P,Lee U.Mean and volatility spillovers across major national stock markets:further empirical evidence[J].Journal of Financial Research,1993,16:337～350.
[133] Bae K,Karolyi G.Good news,bad news and international spillovers of stock return volatility between Japan and the U S,Pacific Basin[J].Finance Journal,1994,2:405～438.
[134] Engle R,Kroner K.Multivariate Simultaneous GARCH[J].Econometric Theory,1995,11:122～150.
[135] Koutmos G,Booth G.A symmetric volatility transmission in international stock markets[J].Journal of International Money and Finance,1995,14:7 47～762.
[136] Booth G,Martikainen T and Yiuman T.Price and Volatility Spillovers in Scandinavian stock markets[J].Journal of Banking and Finance,1997,21:811～823.
[137] Engle R F.Dynamic conditional correlation:a simple class of multivariate generalized autoregressive conditional heteroskedasticity models[J].Journal of Business and Economic Statistics,2002,20:339～350.
[138]赵留彦,王一鸣.A,B股之间的信息流动与波动溢出.金融研究[J].2003,280(10):37～52.
[139]谷耀,陆丽娜.沪,深,港股市信息溢出效应与动态相关性[J].数量经济技术经济研究,2006,8:142～151.
[140]方毅,张屹山.国内外金属期货市场“风险传染”的实证研究[J].金融研究,2007,323(5):133～146.
[141]赵华.人民币汇率与利率之间的价格和波动溢出效应研究[J].金融研究,,2007,321(3):41～49.
[142]吴文锋,刘太阳,吴冲锋.上海与伦敦期铜市场之间的波动溢出效应研究[J].系统工程理论方法应用,2007,3:111～115.
[143] Ripley D M.Systematic elements in the linkage of national stock market indices[J].Review of Economics and Statistics,1973,55:356～361.
[144] Panton V,Parker and Joy.Comovement of international equity markets:a taxonomic approach[J].Journal of Financial and Quantative Analysis,1976,415～432.
[145] Engle R F , Granger C W J . Co-integration and error correction: representation,estimation and testing[J].Econometrica,1987,55(2):251～276.
[146] Eun C,Shim S.International transmission of stock price movements[J].Journal of Financial and Quantitative Analysis,1989,24:241～256.
[147] Jeon B and Von Furstenberg G. M.Growing international co-movements in stock price indexes[J].Quarterly Review of Economics and Business,1990,30:15～30.
[148] Tay,S P,Zhu,Z.Correlations in returns and volatilities in Pacific-Rim stock markets[J].Open Economies Review,2000,11:27～47.
[149] Zhang R F, Zou Q W, Chen J. Common volatility spillover analysis and empirical study on the financial market based on the independent components[C]. Proceedings of 2006 International conference on Management Science & Engineering ,2006:1714～1718.(EI收录: 9264009)
[150]张瑞锋,张世英.唐勇.金融市场波动溢出分析及实证研究[J].中国管理科学,2006,14(5):14～22.
[151] Zhang R F,Zou Q W, Zhang S Y.Volatility spillover analysis and empirical study on the financial market based on copula theory [C].Proceedings of 2007 International conference on Management Science & Engineering ,2007:1874～1881.(ISTP收录)
[152] Black F.Capital market equilibrium with restricted borrowing[J].Joumal of Business,1972,45:444～454.
[153] Mayers D.Non-marketable assets and capital market equilibrium under uncertainty[C].Studies in the Theory of Capital Markets,Praeger Publishers,1972.
[154] Merton,Robert C.Continuous-time Finance[M].Blackwell Publishers,1990.
[155] Breeden,Douglas T.An intertemporal asset pricing model with stochastic consumption and investment opportunities[J].Journal of Financial Economics,1979,7:265～296.
[156] Roll R,Ross S A.An empirical investigation of the arbitrage pricing theory[J],Journal of Finance,1980,35:1073～l103.
[157] Fama E F,French K R.The cross-section of expected stock returns[J].Journal of Finance,1992,4:427～465.
[158]陈小悦,孙爱军.CAPM在中国股市的有效性检验[J].北京大学学报(哲学社会科学版),2000(4):37～42.
[159]李和金,李湛.上海股票市场资本资产定价模型实证检验[J].预测,2000,5:75～78.
[160]陈浪南,屈文洲.资本资产定价模型的实证研究[J].经济研究,2000,4:26～34.
[161] Roll R.A critique of the asset pricing theory’tests:part 1.JournaI of Financilal Economics.1977,4:129～176.
[162] Dyson F.Statistical theory of the energy levels of complex systems i–iii[J].Math. Phys,1962,3:140～175.
[163] Mehta M,Dyson F.Statistical theory of the energy levels of complex systems iv[J].Math. Phys,1963,4(5):713～719.
[164] Dyson F,Mehta M.Statistical theory of the energy levels of complex systems v[J].Math Phys,1963,4(5):701～712.
[165] Plerou V,Gopikrishnan P,Rosenow B,Amaral L,Stanley H E.Universal and non-universal properties of cross-correlations in financial time series[J].Phys Rev Lett,1999,83(7):1471～1474.
[166] Plerou V,Gopikrishnan P,Rosenow B,Amaral L,Stanley H E.Econophysics:financial time series from a statistical point of view[J].Physica A, 2000,279:443～456.
[167] Plerou V,Gopikrishnan P,Rosenow B,Amaral L,Stanley H E.A random matrix theory approach to financial cross-correlations[J],Physica A ,2000,287:374～382.
[168] Ghashghaie S,Breymann W,Peinke J,Taikner P,Dodge Y.Turbulent cascades in foreign exchange market[J].Nature,1996,381:767～770.
[169] Mantegna R N,Stanley H E.Turbulence and financial markets[J].Nature,1996,383:587～588.
[170] Mantegna R N,Stanley H E.Stock market dynamics and turbulence:paralell analysis of fluctuation phenomena[J].Physica A,1997,239:255～266.
[171] Potter M , Cont R , Bouch J P . Financail market as adaptive ecosystem[J].Europhys Lett,1998,41:239～242.
[172] Farmer J D.Market force,ecology and evolution[J]Adaporg preprint server 981,2005.
[173] Plerou V,Gopikrishnan P,Rosenow B,Amaral L,Guhr T,Stanley H E . Collective behaviour of stock price movements : a random matrix approach[J].Physica A,2001,299:175～180.
[174] BouyéE,Durrleman V,Nikeghbali A,et al.Copula:an open fields for risk management.Working Paper of Financial Econometrics Research Centre,City University Business School,London,2001.
[175] Alexander C O . Volatility and correlation : methods , models and applications[M].Risk Management and Analysis: Measuring and Modeling Financial Risk(C O Alexander,Ed)Wiley.
[176] Hamao Y,Masulis R W,Ng V K. Correlation in price changes and volatility across international stock markets[J].Review of Financial Studies, 1990,2(3):281～307.
[177] Sola M,Spagnolo F,Spagnolo N.A test for volatility spillovers[J].Economics Letters,2002,76:77～84.
[178]王海燕,杨方廷,刘鲁.标准化系数与偏相关系数的比较与应用[J].数量经济技术经济研究,2006,9:150～155.
[179]刘建华,赵晓波,卢红梅.多货币资产管理风险度量[J].上海金融,2004,7:38～41.
[180]陈东一,傅绍文.改革以来我国物价波动实证分析[J].山西财经大学学报,2003,25(4):35～37.
[181]陈华友.基于相关系数的优性组合预测模型研究[J].系统工程学报,2006,21(4):353～360.
[182]王政.全球近50年气温波动分析[J].数理统计与管理,2004,23(4):1～6.
[183] Anderson T W.Introduction to Multivariate Statistical Analysis(2d ed),NewYork:John Wily,1984.
[184] Bollerslev T . Generalized autoregressive conditional heteroskedasticity[J]. Journal of Economics,1986,,31:307～327.
[185] Engle R F.Autoregressive heteroskedasticity with estimation of the variance of U K inflation[J].Econometrica,1982,50:987～1008.
[186] Engle R F , Bollerslev T . Modeling the persistence of conditional variances[J].Econometric Review,1986,5:1～50.
[187] Nelson D B . Conditional heteroskedasticity in asset returns : a new approach[J].Econometrica,1991,59:347～370.
[188] Baillie R T,Bollerslev T,Mikkelsen H O.Fractionally integrated generalized autoregressive conditional heteroskedasticity[J].Journal of Econometrics,1996,74:3～30.
[189] Bollerslev T,Engle R F,Wooldridge J.A capital asset pricing model with time varying covariances[J].Journal of Political Economy,1988,96:116～131.
[190]张世英,柯珂.分整增广GARCH-M模型[J].系统工程学报,2003,18(1):16～24.
[191] Bollerslev T , Engle R F . Common persistence in conditional Variances[J].Economitrica,1993,61(1):167～186.
[192] Ding Zh X,Granger C W J.Modeling volatility Persistence of speculative returns:a new approach[J].Journal of Econometrics,1996,73:185～215.
[193] Li Han-dong, Zhang Shi-ying.Common persistence and error-correctionmodel in conditional variance[J].Journal of System Science and System Engineering, 2001,10(3):257～264.
[194]徐绪松,马莉莉,陈彦斌.我国上海股票市场GARCH效应实证研究[J].武汉大学学报(理学版),2002,48(3):293～296.
[195]皮天雷.我国沪市波动聚集性GARCH效应的实证研究[J].管理科学,2003,16(6):31～35.
[196] Anderson T G,Bollerslev T,Diebold F,Labys P.Exchange Rate Returns Standardized by Realized Volatility are (nearly)Gaussian[J].Multinational Finance Journa1,2000,(4):159～179.
[197]郭名媛,张世英.赋权已实现波动及其长记忆性,最优频率选择[J].系统工程学报,2006,21(6):568～573.
[198]唐勇,张世英.已实现波动和已实现极差波动的比较研究[J].系统工程学报,2007,22(4):437～442.
[199]韩清,刘永刚.序列相关的微观结构噪声估计[J].数量经济技术经济研究,2007,4:92～102.
[200] Fama,Eugene F.Efficient capital markets:a review of theory and empirical work [J].Journal of Finance 1970,25 (2):383～417.
[201] Plerou V,Gopikrishnan P,Rosenow B,Amaral L,Guhr T,Stanley H E. A random matrix approach to cross-correlations in financial data[J].Phys Rev E,2002,65(6):1～18.
[202] Colon T,Ruskin H J,Crane M.Random matrix theory and fund of funds portfolio optimization[J].Physica A,2007,382:565～576.
[203] Rosario N Mantegna,H Eugene Stanley,封建强(译),匡宏波(译).An introductong to econophysics[M].北京:中国人民大学出版社,2005