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:Analytical Methods,SpringerVerlag,New York,198847 Devaney R.,A First Course in Chaotic Dynamical Systems,AddisonWesley Publish Company,Inc.,199248 Albin,P.,Approximations of Cooperative Equilibrate in MultiPerson Prisoner’s Dilemma Played by Cellular Automata,Math. Social Sciences, 1992,, pp29331949 Albin. P. Microeconomics Foundations of Cyclical Irregularities or Chaos. Math. Social Sciences, 1987,, pp18521450 Averill M. Law, David Kelton M. Simulation Modeling amp。 Richard E. Quandt. Chaos Models and Their Implications for Forecasting. Eastern Economic Journal, 1985,Vol. XI, 24 Tori De Angelis, Chaos. Chaos Everywhere is What the Theorists Think. APA,199325 Matsuyama, K. Increasing Returns, Industrialization, and Indeterminacy of Equilibrium. Quarterly Journal of Economics, 1991,26 Decoster, G. P. Michael, . Dynamic Implications of Chaotic Monetary Policy. Journal of Macroeconomics, Spring, 1992,, , pp26728727 Saari, D. Mathematical Complexity of Simple Economics. Notice of the AMS, February, 199528 Fischer, P., William R. Smith. Chaos, Fractals, and Dynamics, Marcel Dekker. Inc., New York , 198529 , Mccawley. Chaos, Dynamics amp。 James A. York, Period Three Means Chaos, American Mathematical Monthly,1975,, pp98599219 May, . Simple Mathematical Models with Very Complicated Dynamics. Nature, 1976,, pp9596720 Jensen, R. U. and Urban, R. Chaotic Price Behavior in a Nonlinear Cobweb Model. Mini, Yale University, 198221 Rancl, D, Sxotic. Phenomena in Game amp。 Erratic Behavior. Review of Economic Studies, 1981, 48 : 4594716 Chen, P. Empirical and Theoretical Evidence of Monetary Chaos System Dynamic Review, 1988, 47, : 88967 Hesieh. D. Testing for Nonlinear Dependence in Daily Foreign Exchange Rates. Journal Business, 1989,62(3) : 3393598 Frank, M. and Stengos T. Measuring the Strangeness of Gold and Silver Rates of Return. Review of Economics Studies, 1989,56,: 5535679 Scheinkman, J. A and LeBaron, B. Nonlinear Dynamic and Stock Returns. Journal of Business, 1989, 62, :31133710 Brock, W A, D Hesich and LeBaron. Nonlinear Dynamics, Chaos and Instability: Theory and Empirical. MIT press, Cambridge,199111 Hesieh, and Nonlinear Dynamics: Applications to Financial Markets. Journal of Finance, 1991,47,: 1145118912 Kodres, L. E. and Papell, D,H. Nonlinear Dynamics in the Foreign Exchange Future Market, Working Paper. University of Michigan,199113 Eldridge,R. M and Coleman M. P. The British FTSE100 Index: Chaotically Deterministic or Random? Working Paper. School of Business, Fairfield University,199314 Phillipatos, G. C. Chaotic Behavior in Stock Prices of European Stock Markets: A Comparative Analysis of Major Economic Regions. Working Paper, University of Tennessee,199315 Edgar E. Peters, Chaos and Order in the Capital Markets, John Wiley amp。 Bifurcation in a Macro Model. Journal of Economic Dynamics amp。金融復(fù)雜性的探討方興未艾,只要我們積極進(jìn)取,努力探索,就一定會取得重要的成果。要么用統(tǒng)計方法,要么用混沌方法,難以發(fā)揮定性與定量、數(shù)學(xué)推理與計算機(jī)仿真模擬、局部分析與整體優(yōu)化等各種不同方法的不同特點。(3)對金融市場復(fù)雜性的管理與控制方法缺乏科學(xué)而深入的研究。(2)對復(fù)雜性的機(jī)理缺乏深入的研究。 4 結(jié)論總之,目前第二類方法即復(fù)雜性理論與方法為研究金融證券市場價格波動的復(fù)雜性提供了新的思路和途徑,已成為金融市場復(fù)雜性問題研究的發(fā)展趨勢。總的來看,目前國內(nèi)外關(guān)于證券價格波動研究的方法主要有兩大類,一類是傳統(tǒng)的統(tǒng)計學(xué)方法,另一類就是上述的混沌等非線性理論和方法。P500588(1) 關(guān)聯(lián)維數(shù)(2) 低維混沌孫廣振,王勁松(1995)深圳指數(shù)377(1) 關(guān)聯(lián)維數(shù)(2) 低維混沌林小明,王美今(1997)上證指數(shù)深證指數(shù)10161004(1) 關(guān)聯(lián)維數(shù)(2) 低維混沌 注:(1). 是指Lyapunov指數(shù); (2)BDS是一種統(tǒng)計方法的簡稱。P5002088關(guān)聯(lián)維數(shù)低維混沌Brocket,Hinich amp。 Samp。P5001500(1) BDS方法(2) 關(guān)聯(lián)維數(shù)低維混沌Brock amp。他們得出的結(jié)論是:迪維西貨幣總量在M2和M3水平上是混沌的。之后,有越來越多的學(xué)者開始運用混沌等復(fù)雜性科學(xué)方法研究經(jīng)濟(jì)和金融系統(tǒng),[2][3],[36],May[19],Benhabib[4][5], Shafer, Wolff, Woodford, Deneekere, Poliman 等人在這方面做了不少工作。其主要學(xué)術(shù)觀點