基于随机规划动态投资组合中的情景元素生成研究
|
摘要
随机规划模型作为一个强大的工具被广泛地应用到资产配置、资产负债管理以及投资组合管理等金融领域。随机规划需要生成大量的情景元素来模拟未来的不确定性,以此构建情景树作为随机优化模型的输入,得到出模型的全局最优解,并据此给金融规划提供决策建议。因此,不确定性的准确刻画非常重要,其决定了多阶段投资组合决策成败。本文就随机规划中情景生成模型进行了深入研究,主要研究工作及结论如下:
1、构建了基于GARCH的情景生成模型。
GARCH族模型能很好地刻画金融资产收益的“波动率聚从”,“尖峰厚尾”及“不对称效应”现象。本文利用GARCH模型的突出优点,针对不同类别的资产,建立了相应的AR模型及GARCH模型用于情景生成。主要的研究工作包括四个方面:一元GARCH情景生成模型的研究;多元GARCH情景生成模型的研究;对一元GARCH和多元GARCH模型生成的随机情景质量进行了比较;构建了一个2阶段情景树。
数值研究发现:一元和多元GARCH模型生成情景的累计概率分布与历史数据较为接近,这表明GARCH模型用于情景生成是可取的。其次,多元GARCH模型生成的情景的累计概率分布要比一元模型更接近历史分布,这反映了多元GARCH模型更适合于资产组合时情景生成,原因是多元GARCH模型由于能把资产收益之间的相关性纳入考虑范围,更符合实际情形。不足之处是,多元GARCH模型结构复杂,参数估计困难,当组合资产间的相关性较低时,可考虑一元GARCH模型作为其替代。
2、单变量的矩匹配情景模型生成研究。
Hoyland和Wallace最初提出了矩匹配法生成情景的一般框架,但存在许多缺陷,如局部最优解,存在套利等。本研究改进了其模型,主要做了三方面的工作:单变量的矩匹配情景生成模型研究;套利机会的排除方法研究;历史情景描述性特征的反映;给出了另一种矩匹配情景生成的思路。
单变量的矩匹配模型,以情景的概率作为优化模型的决策变量,通过逼近历史收益序列的各阶中心矩,生成单阶段情景树,然后进一步结合向量自回归模型生成多阶段情景生成。优化模型中增加了一个约束可以有效解决生成情景的描述性特征问题。此外,把收益区间适当剖分一般可避免套利的发生。
第二种方法的思路是每次只产生一个随机变量的离散边际分布,然后在所有离散边际分布的基础上生成联合分布的结果。然后运用各种变换迭代逼近目标矩和相关矩阵。实证研究表明,该方法不仅可以避免大量的数值计算,而且得到的情景取得和历史数据较为吻合的统计特征。
3、基于聚类情景生成的研究及应用
K-均值聚类法可以对大量的数据进行剖分,建立一个单水平的类集,可以将样本数据集剖分成K个互相独立的类,可以被用来构建资产收益情景。本部分研究应用此算法,进行情景生成的尝试,并与矩匹配法生成的情景进行统计意义上的对比。研究表明,K均值聚类法尽量从历史数据的角度出发,挖掘不同资产的收益之间的相关关系;并且给出了只要增加一个情景就可以避免套利的简便易行的线性规划方法。该情景生成方法除了具有矩匹配情景生成方法的优点外,还在对统计特征的刻画上有所改进,能以更少的情景更精确地刻画统计特征。这为选取少量的情景以降低问题的规模奠定了基础,更重要的是为多阶段情景生成引入了一种全新的思路。
4、向量自回归(VAR)模型的情景生成研究及应用
向量自回归模型是金融数据分析中一种常用的模型,常用于预测相互联系的时间序列系统及分析随机扰动对变量系统的动态冲击。本文做了利用VAR模型生成情景的尝试,主要工作如下:构建了包含四个股指收益的VAR模型;基于蒙塔卡罗模拟的情景生成生;多元GARCH模型与VAR模型所生成情景在统计意义上比较;应用VAR建立了一个2阶段的情景树。
研究表明:VAR生成情景在统计意义上较多元GARCH更为可靠,其情景的累计概率分布更接近于历史数据。此外,VAR模型结构较多元GARCH简单,除了体现变量间的相关性,还能很好地反映不同决策阶段的相关性,是一种更优良的情景生成技术。
5、基于Copula函数的情景生成。
Copula函数有三个优点:多元随机变量的联合分布灵活构造,非线性相关性的准确描述及收益非正态分布的支持,这些优点利于构建更准确的情景生成模型。本部分做的工作:给出一个基于Copula函数,GARCH模型及极值理论的一个多资产收益情景生成步骤。将此方法得到情景与VAR,聚类法进行统计意义上的比较工作。研究表明,此方法所生成情景的在统计特征上最接近历史数据,是最为可靠的情景生成方法。
Stochastic Programming Model (SPM), as a powerful tool, has been widely used to such financial fields as asset allocation, Asset and liability management (ALM), and securities' portfolio management and so on. SPM need generate many scenarios simulating future uncertainty of which scenario tree acted as input to stochastic optimization is constructed on basis. The global optimal solution of model is the basis of decision-making advices for financial programming. So, the description of uncertain economic scenario plays a great role in the success of the decision-making in multistage investment portfolio. This paper focuses on study of several models for scenario generation. The main research work and conclusions is as following:
1、building the scenario generation model based on GARCH model.
GARCH family models can depicts the following phenomena of asset return in financial market: volatility clustering, non-asymmetric, leptokurtic features. The paper utilizes these advantages to build the corresponding AR and GARCH models according to the respective asset kinds' features. The main work done here includes four aspects: scenario generation model based on univariate GARCH model. Scenario generation model based on multivariate GARCH model. Comparison of the two kinds of models in statistics. Construction of two-period scenario tree.
The numerical result shows that the two kinds of GARCH models can produce scenarios with similar statistical attributes to historical data which tells us that the GARCH family model is sufficient to scenario generation. Secondly, the multivariate GARCH model has a better performance than the univariate one maybe for the reason that it can take the correlation among the assets into consideration. However, multivariate GARCH model also has a disadvantage, much too complex model structure and difficult parameter estimation. Univariate GARCH model can replace multivariate one when the correlation among assets are small.
2. Single variable moment-matching scenario generation model.
Hoyland and Wallace firstly give a common framework to generate scenario based on moment-matching which builds a scenario tree by solving a non-linear optimization model and getting the value and probability of scenario. It has some pitfalls such as local optimal solution and arbitrage opportunity existence and so on. The work here improves the above model which includes three aspects: study of Single variable moment-matching scenario generation model; how to avoid the arbitrage opportunity; how to depict the descriptive features and another idea of scenario generation based on moment-matching.
Single variable moment-matching scenario generation model takes the probability of the scenario's value as the variable decided and construct the single-period scenario tree by approaching the four center moment of historical return data and then generate multistage tree with the help of VAR model. The article adds a constraint to solve the problem of 'descriptive feature' ignored in scenario generation in the long term. Besides the above, the idea of 'partition of return interzone' assures that it can avoid arbitrage opportunity.
The second way is to produce one random variable's discrete marginal distribution once and then produce a joint distribution on the basis of all the produced discrete marginal distribution, finally, approaches the aimed moment and correlation matrix by all kinds of transforms. Empirical study shows that this way avoid vast numerical computation and can get the scenario with much similar statistical feature of the historical return.
3. Research on generating scenario by clustering and application.
K-means clustering can partition large set of data and build a single-level class, dividing the sample data into K independent clusters as the asset return scenario. The research work here tries this way to generate scenarios and compare it with the way of moment-matching statistically. The result here shows that this method tries not to rely on model to produce scenario but to find the correlation between asset returns from historical data. At the same time, the article gives a linear programming method that adding a scenario in order to avoid arbitrage. The empirical study shows that the way not only has the advantage of moment-matching way, but also has improved in depicting statistical features, which can much more accurately depict statistical features through much less scenarios. The methods lay the foundation for decreasing the size of problems by much less scenario, especially introduces a new idea for multistage scenario generation.
4、Research on scenario generation based on VAR and its application
VAR model is a usual way for financial data analyzing and often used to forecast connected time serials system and analyzes dynamic impulsion to variable system by random disturbance. The research work here includes construction of proper VAR model of four indexes' return; Production a lot of scenarios by Monte Carlo simulation, Comparison of the effect between VAR and multivariate GARCH model; Constructing a 2-period scenario tree.
The research result shows that VAR models performs better than multivariate GARCH model for its CDF is nearer to historical data than the multivariate GARCH model. Besides that, VAR models are simpler. It not only demonstrates the correlation among variables and periods. So it is a excellent way for scenario generation.
5. Scenario generation based on Copula function.
Copula function mainly has three advantages as follows: it can flexibly construct multi-dimension random variable joint distribution; it can accurately depict nonlinear correlation; It can can overcome the limitation of the normal distribution hypothesis of assets return. Here this article does the following research work: Bring forward a comprehensive way to generate scenarios based on Copula function, GARCH model and extreme value theory; Compare its scenario effect with VAR and clustering. The numerical test shows that the way proposal by us is a more reliable method than the other two ones.
1、构建了基于GARCH的情景生成模型。
GARCH族模型能很好地刻画金融资产收益的“波动率聚从”,“尖峰厚尾”及“不对称效应”现象。本文利用GARCH模型的突出优点,针对不同类别的资产,建立了相应的AR模型及GARCH模型用于情景生成。主要的研究工作包括四个方面:一元GARCH情景生成模型的研究;多元GARCH情景生成模型的研究;对一元GARCH和多元GARCH模型生成的随机情景质量进行了比较;构建了一个2阶段情景树。
数值研究发现:一元和多元GARCH模型生成情景的累计概率分布与历史数据较为接近,这表明GARCH模型用于情景生成是可取的。其次,多元GARCH模型生成的情景的累计概率分布要比一元模型更接近历史分布,这反映了多元GARCH模型更适合于资产组合时情景生成,原因是多元GARCH模型由于能把资产收益之间的相关性纳入考虑范围,更符合实际情形。不足之处是,多元GARCH模型结构复杂,参数估计困难,当组合资产间的相关性较低时,可考虑一元GARCH模型作为其替代。
2、单变量的矩匹配情景模型生成研究。
Hoyland和Wallace最初提出了矩匹配法生成情景的一般框架,但存在许多缺陷,如局部最优解,存在套利等。本研究改进了其模型,主要做了三方面的工作:单变量的矩匹配情景生成模型研究;套利机会的排除方法研究;历史情景描述性特征的反映;给出了另一种矩匹配情景生成的思路。
单变量的矩匹配模型,以情景的概率作为优化模型的决策变量,通过逼近历史收益序列的各阶中心矩,生成单阶段情景树,然后进一步结合向量自回归模型生成多阶段情景生成。优化模型中增加了一个约束可以有效解决生成情景的描述性特征问题。此外,把收益区间适当剖分一般可避免套利的发生。
第二种方法的思路是每次只产生一个随机变量的离散边际分布,然后在所有离散边际分布的基础上生成联合分布的结果。然后运用各种变换迭代逼近目标矩和相关矩阵。实证研究表明,该方法不仅可以避免大量的数值计算,而且得到的情景取得和历史数据较为吻合的统计特征。
3、基于聚类情景生成的研究及应用
K-均值聚类法可以对大量的数据进行剖分,建立一个单水平的类集,可以将样本数据集剖分成K个互相独立的类,可以被用来构建资产收益情景。本部分研究应用此算法,进行情景生成的尝试,并与矩匹配法生成的情景进行统计意义上的对比。研究表明,K均值聚类法尽量从历史数据的角度出发,挖掘不同资产的收益之间的相关关系;并且给出了只要增加一个情景就可以避免套利的简便易行的线性规划方法。该情景生成方法除了具有矩匹配情景生成方法的优点外,还在对统计特征的刻画上有所改进,能以更少的情景更精确地刻画统计特征。这为选取少量的情景以降低问题的规模奠定了基础,更重要的是为多阶段情景生成引入了一种全新的思路。
4、向量自回归(VAR)模型的情景生成研究及应用
向量自回归模型是金融数据分析中一种常用的模型,常用于预测相互联系的时间序列系统及分析随机扰动对变量系统的动态冲击。本文做了利用VAR模型生成情景的尝试,主要工作如下:构建了包含四个股指收益的VAR模型;基于蒙塔卡罗模拟的情景生成生;多元GARCH模型与VAR模型所生成情景在统计意义上比较;应用VAR建立了一个2阶段的情景树。
研究表明:VAR生成情景在统计意义上较多元GARCH更为可靠,其情景的累计概率分布更接近于历史数据。此外,VAR模型结构较多元GARCH简单,除了体现变量间的相关性,还能很好地反映不同决策阶段的相关性,是一种更优良的情景生成技术。
5、基于Copula函数的情景生成。
Copula函数有三个优点:多元随机变量的联合分布灵活构造,非线性相关性的准确描述及收益非正态分布的支持,这些优点利于构建更准确的情景生成模型。本部分做的工作:给出一个基于Copula函数,GARCH模型及极值理论的一个多资产收益情景生成步骤。将此方法得到情景与VAR,聚类法进行统计意义上的比较工作。研究表明,此方法所生成情景的在统计特征上最接近历史数据,是最为可靠的情景生成方法。
Stochastic Programming Model (SPM), as a powerful tool, has been widely used to such financial fields as asset allocation, Asset and liability management (ALM), and securities' portfolio management and so on. SPM need generate many scenarios simulating future uncertainty of which scenario tree acted as input to stochastic optimization is constructed on basis. The global optimal solution of model is the basis of decision-making advices for financial programming. So, the description of uncertain economic scenario plays a great role in the success of the decision-making in multistage investment portfolio. This paper focuses on study of several models for scenario generation. The main research work and conclusions is as following:
1、building the scenario generation model based on GARCH model.
GARCH family models can depicts the following phenomena of asset return in financial market: volatility clustering, non-asymmetric, leptokurtic features. The paper utilizes these advantages to build the corresponding AR and GARCH models according to the respective asset kinds' features. The main work done here includes four aspects: scenario generation model based on univariate GARCH model. Scenario generation model based on multivariate GARCH model. Comparison of the two kinds of models in statistics. Construction of two-period scenario tree.
The numerical result shows that the two kinds of GARCH models can produce scenarios with similar statistical attributes to historical data which tells us that the GARCH family model is sufficient to scenario generation. Secondly, the multivariate GARCH model has a better performance than the univariate one maybe for the reason that it can take the correlation among the assets into consideration. However, multivariate GARCH model also has a disadvantage, much too complex model structure and difficult parameter estimation. Univariate GARCH model can replace multivariate one when the correlation among assets are small.
2. Single variable moment-matching scenario generation model.
Hoyland and Wallace firstly give a common framework to generate scenario based on moment-matching which builds a scenario tree by solving a non-linear optimization model and getting the value and probability of scenario. It has some pitfalls such as local optimal solution and arbitrage opportunity existence and so on. The work here improves the above model which includes three aspects: study of Single variable moment-matching scenario generation model; how to avoid the arbitrage opportunity; how to depict the descriptive features and another idea of scenario generation based on moment-matching.
Single variable moment-matching scenario generation model takes the probability of the scenario's value as the variable decided and construct the single-period scenario tree by approaching the four center moment of historical return data and then generate multistage tree with the help of VAR model. The article adds a constraint to solve the problem of 'descriptive feature' ignored in scenario generation in the long term. Besides the above, the idea of 'partition of return interzone' assures that it can avoid arbitrage opportunity.
The second way is to produce one random variable's discrete marginal distribution once and then produce a joint distribution on the basis of all the produced discrete marginal distribution, finally, approaches the aimed moment and correlation matrix by all kinds of transforms. Empirical study shows that this way avoid vast numerical computation and can get the scenario with much similar statistical feature of the historical return.
3. Research on generating scenario by clustering and application.
K-means clustering can partition large set of data and build a single-level class, dividing the sample data into K independent clusters as the asset return scenario. The research work here tries this way to generate scenarios and compare it with the way of moment-matching statistically. The result here shows that this method tries not to rely on model to produce scenario but to find the correlation between asset returns from historical data. At the same time, the article gives a linear programming method that adding a scenario in order to avoid arbitrage. The empirical study shows that the way not only has the advantage of moment-matching way, but also has improved in depicting statistical features, which can much more accurately depict statistical features through much less scenarios. The methods lay the foundation for decreasing the size of problems by much less scenario, especially introduces a new idea for multistage scenario generation.
4、Research on scenario generation based on VAR and its application
VAR model is a usual way for financial data analyzing and often used to forecast connected time serials system and analyzes dynamic impulsion to variable system by random disturbance. The research work here includes construction of proper VAR model of four indexes' return; Production a lot of scenarios by Monte Carlo simulation, Comparison of the effect between VAR and multivariate GARCH model; Constructing a 2-period scenario tree.
The research result shows that VAR models performs better than multivariate GARCH model for its CDF is nearer to historical data than the multivariate GARCH model. Besides that, VAR models are simpler. It not only demonstrates the correlation among variables and periods. So it is a excellent way for scenario generation.
5. Scenario generation based on Copula function.
Copula function mainly has three advantages as follows: it can flexibly construct multi-dimension random variable joint distribution; it can accurately depict nonlinear correlation; It can can overcome the limitation of the normal distribution hypothesis of assets return. Here this article does the following research work: Bring forward a comprehensive way to generate scenarios based on Copula function, GARCH model and extreme value theory; Compare its scenario effect with VAR and clustering. The numerical test shows that the way proposal by us is a more reliable method than the other two ones.
引文
[1] Ang A, Chen J. (2002). Asymmetric correlation of equity portfolio. Journal of Financial Economics, 63(3):443-494.
[2] B.Deler and B. L. Nelson (2000). Modeling and generating multivariate time series with arbitrary marginal using an autoregressive technique. Technical report, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois. 27-34.
[3] Berkelaar, A., H. Hoek, and A. Lucas (1999). Arbitrage and sampling uncertainty in financial stochastic programming models. Econometric Institute Report147, Erasmus University Rotterdam, Netherlands.47-63.
[4] Bertsekas. D.P. (1987). Dynamic programming: Determistic and stochastic. Englewood Cliffs: Prentice-Hall.
[5] Birge, J.R.and F.Louveaux (1997). Introduction to stochastic programming. New York: Springer-Verlag.
[6] Boender, G. C. E. (1999). A Hybrid simulation/optimization scenario model for asset/liability management. European Journal of Operational Research, 99,126-135.
[7] Bogentoft, E., H.E. Romeijn and S. Uryasev (2001). Asset / Liability management for pension funds using CVaR constraints. Journal of Risk Finance, 3,57-71.
[8] Bolleslev T, Baillie R T. (1990).A Multivate generalized ARCH approach to modeling Risk Premia in forward foreign exchange rate markets. Journal of international Money and Finance, 9(3): 309-32
[9] Bolleslev, T. (1986).Generalized Autoregressive Conditional heteroskedasticity. Journal of Econometrics.31:307-327.
[10] Bouye E, Durrleman V, Nikeghbali A, et al. (2001).Copula: An open field for risk management. Working Paper of Financial Econometrics Research Centre, City University Business School, London, 37-40.
[11] Carifio, D. and W. T. Ziemba (1998). Formulation of the Russell-Yasuda Kasai financial planning model. Operations Research, 46,433-449
[12] Carino, D.R., Myers, D.H., Ziemba, W.T. (1998). Concepts, technical issues, and uses of the Russell-Yasuda Kasai financial planning model. Operations Research 46 (4), 450-462
[13] Carino, D., Kent, T., Myers, D.H., Stacy, C., Sylvanus, M., Turner, A.L., Watanabe, K., Ziemba, W.T. (1998). The Russell-Yasuda Kasai model: An asset/liability model for a Japanese insurance company using multistage stochastic programming. Worldwide Asset and Liability Modeling.
[14] Carino, D., Kent, T., Myers, D.H., Stacy, C., Sylvanus, M., Turner, A.L., Watanabe, K., Ziemba, W.T. (1998). Formulation of the Russell-Yasuda Kasai financial planning model Operations Research, 46,433-449.
[15] C. David Vale and Vincent A. (1983). Maurelli. Simulating multivariate nonnormal distributions. Psychometrika, 48(3):465-471.
[16] Christofides, A., Tanyi, B., Christofides, S., Whobrey, D., Christo3des, N. (1999). The optimal discretisation of probability density functions. Computational Statistics & Data Analysis 31,475-486.
[17] Dempster, M., Thorlacius, A.E. (1998). Stochastic simulation of internal economic variables and asset returns: the Falcon asset model. Proceedings of the 8th International AFIR Colloquium, London Institute of Actuaries, 29-45.
[18] Dert, C. L. (1995). Asset liability management for Pension funds-A multistage Chance Constrained programming Approach. Ph.D Thesis, Erasmus University Rotterdam, Netherlands, 30-32.
[19] Ding Zhuangxin, C. W. J, Granger, and R. F. Engle (1993). A Long Memory Property of Stock Market Return and New Model, Journal of Empirical Finance, 1: 83-106
[20] Dixit, A.K., Pindyck, R. (1994). Investment under Uncertainty. Princeton University Press, Princeton, 7-9.
[21] Dorfman, R., Samuelson, P.A., Solow, R.M. (1958). Linear Programming and Economic Analysis. McGraw Hill, New York, 12-13.
[22] Durrleman, D. Nikeghbali, A. Roncalli, T. (2000). Which copula is the right one?. Working Paper, Groupe de Recherche Operationnelle, Credit Lyonnais,46-48.
[23] Embrechts, P., Lindskog, F., McNeil (2003). A Modeling dependence with copulas and application to risk management. Handbook of heavy Tailed Distribution in Finance, ed. S. Rachev, Elsevier, 329-384
[24] Engle R F. (2001). Dynamic Conditional Correlation- A Simple Class of Multivate GARCH Models. Forthcoming in Journal of Business and Economic Statistics, 2001.
[25] Engle R F. (1982). Autoregressive Conditional Heteroskedasticity with Estimates of the of United Kingdom inflation Econometrica, 50(4):987-1008.
[26] Engle, Robert F, Victor K Ng. (1993). Measuring and Testing the Impact of News on volatility. Journal of Finance, 48:1022-1082.
[27] Engle R F, Sheppard K. (2001). Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH. Working Paper No. 8554, National Bureau of Economic Research.
[28] Fang K.T., S. kotz, and K.W. Ng (1987). Symmetric Multivariate and Related Distributions. London: Chapman and Hall.
[29] Fermanian, J., and Scaillet O. (2003). Nonparametric estimation of copulas for time series. Working papers, 23-39.
[30] G. C. Pflug (2001). Scenario tree generation for multiperiod financial optimization by optimal discretization. Mathematical Programming, 89(2):251-271.
[31] Genest C, Mackay J. (1986). The Joy of Copulas: Bivariate distributions with uniform margins. American Statistician, 40:280-283.
[32] George B. Dantzig and Gerd Infanger (1992). Large-scale stochastic linear programs—importance sampling and Benders decomposition. In Computational and applied mathematics, 111-120.
[33] G Infanger (1994). Planning under Uncertainty: Solving Large-Scale Stochastic Linear Programs. Boyd and Fraser, Danvers.
[34] Glosten, L. R., Jagannathan, and D. Runkle (1993). On the relation Between the Expected Value and Volatility of the Nominal Excess Return on Stocks. Journal of Finance, 48:1779-1901.
[35] Gulpinar N, Rustem B, Settergren R (2001). Simulation and optimization approaches to scenario tree generation. London: Imperial College of Science, Technology and Medicine.
[36] Hamilton, J. D. (1994). Time Series Analysis, Princeton: Princeton University Press.
[37] Hansen, P., Jaumard, B. (1997).Cluster analysis and mathematical programming. Mathematical Programming, 79,191-215.
[38] Harrison, J. M. and D. M. Kreps (1979). Martingales and Arbitrage in multiperiod securities markets. Journal of Economic Theory, 20,381-408
[39] Hibiki, N. (2000). Multi-period stochastic programming models for dynamic asset allocation. In: Proceedings of the 31st ISCIE International Symposium on Stochastic Systems Theory and its Applications, 37-42.
[40] Hoyland, K. and S. W. Wallace (2001).Generating scenario trees for multistage decision problems, Management Science, 47,295-307
[41] Hoyland, K., Kaut, M., Wallace, S.W. (2003). A heuristic for moment-matching scenario generation. Computational Optimization and Applications, 44,169—185.
[42] IBM Corp (1998). IBM Optimization Library Stochastic Extensions Users Guide.
[43] Jitka Dupacova, Nicole Growe-Kuska, and Werner Romisch (2003). Scenario reduction in stochastic programming. Mathematical Programming. 95(3):493-511.
[44] Jitka Dupacova, Giorgio Consigli, and Stein W. Wallace (2000). Scenarios for multistage stochastic programs. Ann. Oper Res. 100:25-53
[45] J. L. Higle and S. Sen (1991). Stochastic decomposition: An algorithm for two-stage linear programs with recourse. Mathematics of Operations Research. 16:650-669.
[46] Jain, A. K., M. N. murty, and P. J. Flynn (1999). Data Clustering: A review ACM Computing Surveys.31,264-323
[47] James E. Smith (1993). Moment methods for decision analysis. Management Science. 39(3), 340-358.
[48] Jamshidian F, Zhu Y. (1997). Scenario simulation: theory and methodology. Finance Stochastic. 1:43-67.
[49] Johan Lyhagen (2001). A method to generate multivariate data with moments arbitrary close to the desired moments. Working paper 481, Stockholm School of Economics
[50] Joskow PL, Schmalensee R. (1983). Markets for power: an analysis of electrical utility deregulation. Cambridge, MA: MIT Press.
[51] Kall, P. and S. W. Wallace (1994).Stochastic Programming, Chichester: John Wiley&Sons
[52] Kjetil H(?)yland, Michal Kaut, and Stein W. Wallace (2003). A heuristic for moment-matching scenario generation. Computational Optimization and Applications, 24(2-3): 169-185.
[53] Klaassen P. (2002): Comment on Generating scenario trees for multistage decision problems. Management Science, 48,1512-1516.
[54] Klaassen, P. (1997). Discretized reality and spurious profits in stochastic programming models for asset liability management. European Journal of Operational Research 101, 374-392.
[55] Klaassen, P. (1998). Financial asset-pricing theory and stochastic programming models for asset-liability management: a synthesis. Management Science, 44,31-48.
[56] K. H(?)yland and S. W. Wallace (2001). Generating scenario trees for multistage decision problems. Management Science, 47(2):295-307.
[57] Kouwenberg, R. (2001). Scenario generation and stochastic programming models for asset liability management. European Journal of Operational Research 134 (2), 279-293.
[58] Kouwenberg, R. (2001). Scenario generation and stochastic programming models for asset liability management, European Journal of Operational Research, 134,51-64
[59] Kouwenberg, R., J.Gondzio, and A. C. F. Vorst (2003). Hedging options under Transaction costs and stochastic volatility, Journal of Economic Dynamics and Control, 27,1045-1068
[60] Kouwenberg, R. and T. Vorst (1996).Dynamic portfolio insurance: A stochastic programming approach, Erasmus Center for Financial Research Report9909, Erasmus University Rotterdam. Netherlands.
[61] Kusy, M. I and W. T. Ziemba (1986): A bank asset and liability management Model. Operations Research, 34,356-376
[62] Li. DX (2000). On default correlation: A Copula Function Approach. Journal of Fixed Income, 3,43-54.
[63] Lurie P. M. and Goldberg M. S. (1998).An approximate method for sampling correlated random variables from partially-specified distributions, Management Science, 44 (2), 203218.
[64] M. C. Cario and B.L. Nelson (1997). Modeling and generating random vectors with arbitrary marginal distributions and correlation matrix. Technical report, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois.
[65] Mico Loretan (1997). Generating market risk scenarios using principal components analysis: Methodological and practical considerations. CGFS Publications 7,23-60.
[66] Miller, A. C. and T. R. Rice (1983). Discrete approximation of probability distributions, Management Science, 29,352-362
[67] Mulvey, J.M. (1996). Generating scenarios for the tower Perrin investment system. Interfaces 26,1-13
[68] Mulvey, J. M. and H. Vladimirou (1992). Stochastic network programming for financial planning problems. Management Science, 38,1642-1664.
[69] Mulvey, J.M., GGould, and C.Morgan (2000).An asset and liability management system for Towers Perrin-Tillinghast.Interface, 30,96-114
[70] Mulvey, J.M., Ruszczynski, A. (1995). A new scenario decomposition method for large-scale stochastic optimization. Oper. Res. 43,477-490
[71] Mulvey, J.M., Vladimirou, H. (1992). Stochastic network programming for financial planning problems. Management Science, 38 (11), 1642-1664.
[72]Mulvey, J.M, Roseenbaum, D P, SHRTTY(1999). Theory and methodology-parameter estimation in stochastic scenario generation systems. European Journal of Operational Research, 118,563-577
[73] N. Topaloglou, Vladimirou H., and S. A. Zenios (2002). CVaR models with selective hedging for international asset allocation. Journal of Banking and Finance, 26(7):1535-1561.
[74] N. Gulpinar, B. Rustem, and R. Settergren (2002). Optimization and simulation approaches to scenario tree generation. Journal of Economics Dynamics and Control.24-26.
[75] Nielsen, S., Zenios, SA. (1993). A massively parallel algorithm for nonlinear stochastic network problems. Oper. Res. 41, 319-337
[76] Nelson, Daniel B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica.59:347-370.
[77] Peter Kall and Stein W. Wallace (1994).Stochastic Programming, England: John Wiley &SonsLtd
[78] Pflug, G.Ch. (2001). Scenario tree generation for multiperiod financial optimization by optimal discretization. Mathematical Programming .89,251-271.
[79] P. M. Lurie and M. S. Goldberg. (1998). an approximate method for sampling correlated random variables from partially-specified distributions. Management Science, 44(2):203-218.
[80] Rockefeller, R.T., Wets, R.J.-B. (1991).scenarios and Policy Aggregation in Optimization under Uncertainty.Math.Oper.Res.16,119-147
[81]Roger Halldin(2002).Scenario Trees for Inflow Modeling in Stochastic Optimization for Energy Planning.PhD thesis,Lund University,Sweden.
[82]R.R.P.Kouwenberg(2001).Scenario generation and stochastic programming models for asset liability management.European Journal of Operational Research,134(2):51-64.
[83]Settergren,R.(2000).Manual for foliage.Department of Computing,Imperial College of Technology,Science and Medicine.
[84]Sldar A.(1959).Fonctions derepartition a dimensionset leurs marges.Publication del-Institut de Statistique del-Universit6deParis,8:229-231
[85]Smith,J.E.(1993).Moment methods for decision analysis.Management.Science.39,340-358.
[86]Sobol,I.M.(1967).Thedistribution of points in a cube and the approximateevaluation of integrals.U.S.S.R.Computational Mathematics and Mathematical Physics 7(4),86-112.
[87]Taqqu,M.S.,Willinger,W.(1987).The analysis of 3nite security markets using martingales.Advances in Applied Probability,19,1-25.
[88]Tibiletti L(1997).Beneficial Changes in Random Variables via Copulas:An Application to Insurance.Insurance:Mathematics and Economics.19(2):166
[89]T.Pennanen and M.Koivu(2002).Integration quadratures in discretization of stochastic programs.Stochastic Programming E-Print Series,http://www.speps.info.
[90]Vitoriano,B.,Cerisola,S.,Ramos,A.(2001).Generating scenario trees for hydro inGows.Working Paper.
[91]W.Romisch and H.Heitsch(2003).Scenario reduction algorithms in stochastic programming.Computational Optimization and Applications,24(2-3):187-206.
[92]Yu.Ermoliev(1976).Methods of Stochastic Programming.Nanka,Moscow,In Russian.
[93]Yury M(1992).Ermoliev and Alexei A.Gaivoronski.Stochastic quasigradient methods for optimization of discrete event systems.Ann.Oper.Res.,39(1-4):1-39.
[94]Zakoian,J.M.(1994).Threshold Heteroskedasticity Models.Journal of Economics Dynamics and Control,18:931-944.
[95]Zenios,S.A.,M.R.Holmer,M.Raymond and V-Z.Christiana(1998).Dynamic model for fixed-income portfolio management under uncertainty,Journal of Economic Dynamics and Control,22,1517-1541.
[96]Zhao,Y.G and T.Ziemba(2001).A stochastic programming model using an endogenously determined worst case risk measure for dynamic asset allocation,Mathematical Programming,ser.B,89,293-309.
[97]Ziemba,W.T.and J.M.Mulvey(Eds)(1998).Worldwide Asset and Liability Modeling,Cambridge:Cambridge University Press.
[98]樊智,张世英(2003).多GARCH建模及其在中国股市分析中的应用.管理科学学报.6(2):65-73.
[99]高铁梅(2005).计量经济分析方法与建模:Eviews应用及实例.北京:清华大学出版社.
[100]韩明(2004).Copula一个新的计量经济工具.统计与信息论坛.19(5):15-18.
[101]刘宝旋、赵瑞清(1998).随机规划与模糊规划.北京:清华大学出版社.
[102]刘志东(2003).资产组合风险度量与选择研究.北京:中国矿业大学(北京)管理学院.
[103]李亚静,朱宏泉,彭育威(2003).基于GARCH模型族的中国股市波动行预测.数学的实践与认识.33(11):65-71.
[104]王军武(2004),试论蒙塔卡洛风险分析中的变量相关性问题,国外建材科技,Vol25(3),.
[105]韦艳华,张世英,郭众(2004).金融市场相关程度与相关模式的研究.系统工程学.19(4):355-362.
[106]韦艳华,张世英(2004).金触市场的相关性分析一Copula-GARCH模型及其应用.系统工程.22(4):7-12
[107]韦艳华,张世英,孟利锋(2003).Copula技术及其在金融时间序列分析上的应用.系统工程.21(增刊):41-45.
[108]韦艳华,张世英,孟利锋(2003).Copula理论在金融上的应用.西北农林科技大学学报(社会科学版)3(5):97-101
[109]余萍,龚金国(2005).描述金融市场相关结构的一种新工具-Copula.几东莞理工学院学报.12(5):18-22
[110]张晓庭(2002).我们应该选用什么样的相关指标.条件研究.(9):41-44
[111]张晓庭(2002).连接函数技术与金融风险分析[J].条件研究.(4)
[112][美]詹姆斯.D.汉密尔顿.刘明志译(1999),.时间序列分析.北京:中国社会科学出版社,(2),424.804-805.
[113]张明珠(2005).基于Copula函数对相依部件系统可靠度的度量和改进,许昌学院学报,24(2):14-17.
[114]张尧庭(2002).连接函数(Copula)技术与金融风险分析.统计研究.(4):48-51.
[2] B.Deler and B. L. Nelson (2000). Modeling and generating multivariate time series with arbitrary marginal using an autoregressive technique. Technical report, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois. 27-34.
[3] Berkelaar, A., H. Hoek, and A. Lucas (1999). Arbitrage and sampling uncertainty in financial stochastic programming models. Econometric Institute Report147, Erasmus University Rotterdam, Netherlands.47-63.
[4] Bertsekas. D.P. (1987). Dynamic programming: Determistic and stochastic. Englewood Cliffs: Prentice-Hall.
[5] Birge, J.R.and F.Louveaux (1997). Introduction to stochastic programming. New York: Springer-Verlag.
[6] Boender, G. C. E. (1999). A Hybrid simulation/optimization scenario model for asset/liability management. European Journal of Operational Research, 99,126-135.
[7] Bogentoft, E., H.E. Romeijn and S. Uryasev (2001). Asset / Liability management for pension funds using CVaR constraints. Journal of Risk Finance, 3,57-71.
[8] Bolleslev T, Baillie R T. (1990).A Multivate generalized ARCH approach to modeling Risk Premia in forward foreign exchange rate markets. Journal of international Money and Finance, 9(3): 309-32
[9] Bolleslev, T. (1986).Generalized Autoregressive Conditional heteroskedasticity. Journal of Econometrics.31:307-327.
[10] Bouye E, Durrleman V, Nikeghbali A, et al. (2001).Copula: An open field for risk management. Working Paper of Financial Econometrics Research Centre, City University Business School, London, 37-40.
[11] Carifio, D. and W. T. Ziemba (1998). Formulation of the Russell-Yasuda Kasai financial planning model. Operations Research, 46,433-449
[12] Carino, D.R., Myers, D.H., Ziemba, W.T. (1998). Concepts, technical issues, and uses of the Russell-Yasuda Kasai financial planning model. Operations Research 46 (4), 450-462
[13] Carino, D., Kent, T., Myers, D.H., Stacy, C., Sylvanus, M., Turner, A.L., Watanabe, K., Ziemba, W.T. (1998). The Russell-Yasuda Kasai model: An asset/liability model for a Japanese insurance company using multistage stochastic programming. Worldwide Asset and Liability Modeling.
[14] Carino, D., Kent, T., Myers, D.H., Stacy, C., Sylvanus, M., Turner, A.L., Watanabe, K., Ziemba, W.T. (1998). Formulation of the Russell-Yasuda Kasai financial planning model Operations Research, 46,433-449.
[15] C. David Vale and Vincent A. (1983). Maurelli. Simulating multivariate nonnormal distributions. Psychometrika, 48(3):465-471.
[16] Christofides, A., Tanyi, B., Christofides, S., Whobrey, D., Christo3des, N. (1999). The optimal discretisation of probability density functions. Computational Statistics & Data Analysis 31,475-486.
[17] Dempster, M., Thorlacius, A.E. (1998). Stochastic simulation of internal economic variables and asset returns: the Falcon asset model. Proceedings of the 8th International AFIR Colloquium, London Institute of Actuaries, 29-45.
[18] Dert, C. L. (1995). Asset liability management for Pension funds-A multistage Chance Constrained programming Approach. Ph.D Thesis, Erasmus University Rotterdam, Netherlands, 30-32.
[19] Ding Zhuangxin, C. W. J, Granger, and R. F. Engle (1993). A Long Memory Property of Stock Market Return and New Model, Journal of Empirical Finance, 1: 83-106
[20] Dixit, A.K., Pindyck, R. (1994). Investment under Uncertainty. Princeton University Press, Princeton, 7-9.
[21] Dorfman, R., Samuelson, P.A., Solow, R.M. (1958). Linear Programming and Economic Analysis. McGraw Hill, New York, 12-13.
[22] Durrleman, D. Nikeghbali, A. Roncalli, T. (2000). Which copula is the right one?. Working Paper, Groupe de Recherche Operationnelle, Credit Lyonnais,46-48.
[23] Embrechts, P., Lindskog, F., McNeil (2003). A Modeling dependence with copulas and application to risk management. Handbook of heavy Tailed Distribution in Finance, ed. S. Rachev, Elsevier, 329-384
[24] Engle R F. (2001). Dynamic Conditional Correlation- A Simple Class of Multivate GARCH Models. Forthcoming in Journal of Business and Economic Statistics, 2001.
[25] Engle R F. (1982). Autoregressive Conditional Heteroskedasticity with Estimates of the of United Kingdom inflation Econometrica, 50(4):987-1008.
[26] Engle, Robert F, Victor K Ng. (1993). Measuring and Testing the Impact of News on volatility. Journal of Finance, 48:1022-1082.
[27] Engle R F, Sheppard K. (2001). Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH. Working Paper No. 8554, National Bureau of Economic Research.
[28] Fang K.T., S. kotz, and K.W. Ng (1987). Symmetric Multivariate and Related Distributions. London: Chapman and Hall.
[29] Fermanian, J., and Scaillet O. (2003). Nonparametric estimation of copulas for time series. Working papers, 23-39.
[30] G. C. Pflug (2001). Scenario tree generation for multiperiod financial optimization by optimal discretization. Mathematical Programming, 89(2):251-271.
[31] Genest C, Mackay J. (1986). The Joy of Copulas: Bivariate distributions with uniform margins. American Statistician, 40:280-283.
[32] George B. Dantzig and Gerd Infanger (1992). Large-scale stochastic linear programs—importance sampling and Benders decomposition. In Computational and applied mathematics, 111-120.
[33] G Infanger (1994). Planning under Uncertainty: Solving Large-Scale Stochastic Linear Programs. Boyd and Fraser, Danvers.
[34] Glosten, L. R., Jagannathan, and D. Runkle (1993). On the relation Between the Expected Value and Volatility of the Nominal Excess Return on Stocks. Journal of Finance, 48:1779-1901.
[35] Gulpinar N, Rustem B, Settergren R (2001). Simulation and optimization approaches to scenario tree generation. London: Imperial College of Science, Technology and Medicine.
[36] Hamilton, J. D. (1994). Time Series Analysis, Princeton: Princeton University Press.
[37] Hansen, P., Jaumard, B. (1997).Cluster analysis and mathematical programming. Mathematical Programming, 79,191-215.
[38] Harrison, J. M. and D. M. Kreps (1979). Martingales and Arbitrage in multiperiod securities markets. Journal of Economic Theory, 20,381-408
[39] Hibiki, N. (2000). Multi-period stochastic programming models for dynamic asset allocation. In: Proceedings of the 31st ISCIE International Symposium on Stochastic Systems Theory and its Applications, 37-42.
[40] Hoyland, K. and S. W. Wallace (2001).Generating scenario trees for multistage decision problems, Management Science, 47,295-307
[41] Hoyland, K., Kaut, M., Wallace, S.W. (2003). A heuristic for moment-matching scenario generation. Computational Optimization and Applications, 44,169—185.
[42] IBM Corp (1998). IBM Optimization Library Stochastic Extensions Users Guide.
[43] Jitka Dupacova, Nicole Growe-Kuska, and Werner Romisch (2003). Scenario reduction in stochastic programming. Mathematical Programming. 95(3):493-511.
[44] Jitka Dupacova, Giorgio Consigli, and Stein W. Wallace (2000). Scenarios for multistage stochastic programs. Ann. Oper Res. 100:25-53
[45] J. L. Higle and S. Sen (1991). Stochastic decomposition: An algorithm for two-stage linear programs with recourse. Mathematics of Operations Research. 16:650-669.
[46] Jain, A. K., M. N. murty, and P. J. Flynn (1999). Data Clustering: A review ACM Computing Surveys.31,264-323
[47] James E. Smith (1993). Moment methods for decision analysis. Management Science. 39(3), 340-358.
[48] Jamshidian F, Zhu Y. (1997). Scenario simulation: theory and methodology. Finance Stochastic. 1:43-67.
[49] Johan Lyhagen (2001). A method to generate multivariate data with moments arbitrary close to the desired moments. Working paper 481, Stockholm School of Economics
[50] Joskow PL, Schmalensee R. (1983). Markets for power: an analysis of electrical utility deregulation. Cambridge, MA: MIT Press.
[51] Kall, P. and S. W. Wallace (1994).Stochastic Programming, Chichester: John Wiley&Sons
[52] Kjetil H(?)yland, Michal Kaut, and Stein W. Wallace (2003). A heuristic for moment-matching scenario generation. Computational Optimization and Applications, 24(2-3): 169-185.
[53] Klaassen P. (2002): Comment on Generating scenario trees for multistage decision problems. Management Science, 48,1512-1516.
[54] Klaassen, P. (1997). Discretized reality and spurious profits in stochastic programming models for asset liability management. European Journal of Operational Research 101, 374-392.
[55] Klaassen, P. (1998). Financial asset-pricing theory and stochastic programming models for asset-liability management: a synthesis. Management Science, 44,31-48.
[56] K. H(?)yland and S. W. Wallace (2001). Generating scenario trees for multistage decision problems. Management Science, 47(2):295-307.
[57] Kouwenberg, R. (2001). Scenario generation and stochastic programming models for asset liability management. European Journal of Operational Research 134 (2), 279-293.
[58] Kouwenberg, R. (2001). Scenario generation and stochastic programming models for asset liability management, European Journal of Operational Research, 134,51-64
[59] Kouwenberg, R., J.Gondzio, and A. C. F. Vorst (2003). Hedging options under Transaction costs and stochastic volatility, Journal of Economic Dynamics and Control, 27,1045-1068
[60] Kouwenberg, R. and T. Vorst (1996).Dynamic portfolio insurance: A stochastic programming approach, Erasmus Center for Financial Research Report9909, Erasmus University Rotterdam. Netherlands.
[61] Kusy, M. I and W. T. Ziemba (1986): A bank asset and liability management Model. Operations Research, 34,356-376
[62] Li. DX (2000). On default correlation: A Copula Function Approach. Journal of Fixed Income, 3,43-54.
[63] Lurie P. M. and Goldberg M. S. (1998).An approximate method for sampling correlated random variables from partially-specified distributions, Management Science, 44 (2), 203218.
[64] M. C. Cario and B.L. Nelson (1997). Modeling and generating random vectors with arbitrary marginal distributions and correlation matrix. Technical report, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois.
[65] Mico Loretan (1997). Generating market risk scenarios using principal components analysis: Methodological and practical considerations. CGFS Publications 7,23-60.
[66] Miller, A. C. and T. R. Rice (1983). Discrete approximation of probability distributions, Management Science, 29,352-362
[67] Mulvey, J.M. (1996). Generating scenarios for the tower Perrin investment system. Interfaces 26,1-13
[68] Mulvey, J. M. and H. Vladimirou (1992). Stochastic network programming for financial planning problems. Management Science, 38,1642-1664.
[69] Mulvey, J.M., GGould, and C.Morgan (2000).An asset and liability management system for Towers Perrin-Tillinghast.Interface, 30,96-114
[70] Mulvey, J.M., Ruszczynski, A. (1995). A new scenario decomposition method for large-scale stochastic optimization. Oper. Res. 43,477-490
[71] Mulvey, J.M., Vladimirou, H. (1992). Stochastic network programming for financial planning problems. Management Science, 38 (11), 1642-1664.
[72]Mulvey, J.M, Roseenbaum, D P, SHRTTY(1999). Theory and methodology-parameter estimation in stochastic scenario generation systems. European Journal of Operational Research, 118,563-577
[73] N. Topaloglou, Vladimirou H., and S. A. Zenios (2002). CVaR models with selective hedging for international asset allocation. Journal of Banking and Finance, 26(7):1535-1561.
[74] N. Gulpinar, B. Rustem, and R. Settergren (2002). Optimization and simulation approaches to scenario tree generation. Journal of Economics Dynamics and Control.24-26.
[75] Nielsen, S., Zenios, SA. (1993). A massively parallel algorithm for nonlinear stochastic network problems. Oper. Res. 41, 319-337
[76] Nelson, Daniel B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica.59:347-370.
[77] Peter Kall and Stein W. Wallace (1994).Stochastic Programming, England: John Wiley &SonsLtd
[78] Pflug, G.Ch. (2001). Scenario tree generation for multiperiod financial optimization by optimal discretization. Mathematical Programming .89,251-271.
[79] P. M. Lurie and M. S. Goldberg. (1998). an approximate method for sampling correlated random variables from partially-specified distributions. Management Science, 44(2):203-218.
[80] Rockefeller, R.T., Wets, R.J.-B. (1991).scenarios and Policy Aggregation in Optimization under Uncertainty.Math.Oper.Res.16,119-147
[81]Roger Halldin(2002).Scenario Trees for Inflow Modeling in Stochastic Optimization for Energy Planning.PhD thesis,Lund University,Sweden.
[82]R.R.P.Kouwenberg(2001).Scenario generation and stochastic programming models for asset liability management.European Journal of Operational Research,134(2):51-64.
[83]Settergren,R.(2000).Manual for foliage.Department of Computing,Imperial College of Technology,Science and Medicine.
[84]Sldar A.(1959).Fonctions derepartition a dimensionset leurs marges.Publication del-Institut de Statistique del-Universit6deParis,8:229-231
[85]Smith,J.E.(1993).Moment methods for decision analysis.Management.Science.39,340-358.
[86]Sobol,I.M.(1967).Thedistribution of points in a cube and the approximateevaluation of integrals.U.S.S.R.Computational Mathematics and Mathematical Physics 7(4),86-112.
[87]Taqqu,M.S.,Willinger,W.(1987).The analysis of 3nite security markets using martingales.Advances in Applied Probability,19,1-25.
[88]Tibiletti L(1997).Beneficial Changes in Random Variables via Copulas:An Application to Insurance.Insurance:Mathematics and Economics.19(2):166
[89]T.Pennanen and M.Koivu(2002).Integration quadratures in discretization of stochastic programs.Stochastic Programming E-Print Series,http://www.speps.info.
[90]Vitoriano,B.,Cerisola,S.,Ramos,A.(2001).Generating scenario trees for hydro inGows.Working Paper.
[91]W.Romisch and H.Heitsch(2003).Scenario reduction algorithms in stochastic programming.Computational Optimization and Applications,24(2-3):187-206.
[92]Yu.Ermoliev(1976).Methods of Stochastic Programming.Nanka,Moscow,In Russian.
[93]Yury M(1992).Ermoliev and Alexei A.Gaivoronski.Stochastic quasigradient methods for optimization of discrete event systems.Ann.Oper.Res.,39(1-4):1-39.
[94]Zakoian,J.M.(1994).Threshold Heteroskedasticity Models.Journal of Economics Dynamics and Control,18:931-944.
[95]Zenios,S.A.,M.R.Holmer,M.Raymond and V-Z.Christiana(1998).Dynamic model for fixed-income portfolio management under uncertainty,Journal of Economic Dynamics and Control,22,1517-1541.
[96]Zhao,Y.G and T.Ziemba(2001).A stochastic programming model using an endogenously determined worst case risk measure for dynamic asset allocation,Mathematical Programming,ser.B,89,293-309.
[97]Ziemba,W.T.and J.M.Mulvey(Eds)(1998).Worldwide Asset and Liability Modeling,Cambridge:Cambridge University Press.
[98]樊智,张世英(2003).多GARCH建模及其在中国股市分析中的应用.管理科学学报.6(2):65-73.
[99]高铁梅(2005).计量经济分析方法与建模:Eviews应用及实例.北京:清华大学出版社.
[100]韩明(2004).Copula一个新的计量经济工具.统计与信息论坛.19(5):15-18.
[101]刘宝旋、赵瑞清(1998).随机规划与模糊规划.北京:清华大学出版社.
[102]刘志东(2003).资产组合风险度量与选择研究.北京:中国矿业大学(北京)管理学院.
[103]李亚静,朱宏泉,彭育威(2003).基于GARCH模型族的中国股市波动行预测.数学的实践与认识.33(11):65-71.
[104]王军武(2004),试论蒙塔卡洛风险分析中的变量相关性问题,国外建材科技,Vol25(3),.
[105]韦艳华,张世英,郭众(2004).金融市场相关程度与相关模式的研究.系统工程学.19(4):355-362.
[106]韦艳华,张世英(2004).金触市场的相关性分析一Copula-GARCH模型及其应用.系统工程.22(4):7-12
[107]韦艳华,张世英,孟利锋(2003).Copula技术及其在金融时间序列分析上的应用.系统工程.21(增刊):41-45.
[108]韦艳华,张世英,孟利锋(2003).Copula理论在金融上的应用.西北农林科技大学学报(社会科学版)3(5):97-101
[109]余萍,龚金国(2005).描述金融市场相关结构的一种新工具-Copula.几东莞理工学院学报.12(5):18-22
[110]张晓庭(2002).我们应该选用什么样的相关指标.条件研究.(9):41-44
[111]张晓庭(2002).连接函数技术与金融风险分析[J].条件研究.(4)
[112][美]詹姆斯.D.汉密尔顿.刘明志译(1999),.时间序列分析.北京:中国社会科学出版社,(2),424.804-805.
[113]张明珠(2005).基于Copula函数对相依部件系统可靠度的度量和改进,许昌学院学报,24(2):14-17.
[114]张尧庭(2002).连接函数(Copula)技术与金融风险分析.统计研究.(4):48-51.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |