所謂複雜系統,目前並沒有標準定義。我們可以找到許多文章嘗試要明確的定義它。一般而言,複雜系統是指整體系統特性無法完全由其個別組成份子的特性所解釋。也就是說,在集合眾多個體組成一個龐大的系統後,所呈現的一些特性是組成個體所沒有的。P. W. Anderson [5] 在1972年的文章標題《量多就不一樣 more is




Название所謂複雜系統,目前並沒有標準定義。我們可以找到許多文章嘗試要明確的定義它。一般而言,複雜系統是指整體系統特性無法完全由其個別組成份子的特性所解釋。也就是說,在集合眾多個體組成一個龐大的系統後,所呈現的一些特性是組成個體所沒有的。P. W. Anderson [5] 在1972年的文章標題《量多就不一樣 more is
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價格變動,注意到其極端值出現的機率遠比一般認為的高斯分佈所預測的大。而在使用不同的時間間距匯整價格變動畫成各曲線時,看起來都十分相似。此為使用碎形來描述價格變動的濫觴,也開啟了使用有別於傳統經濟方法研究金融市場的方法。視經濟體為一複雜系統,則是在1987年,由 Kenneth J. Arrow 及一些經濟學家與物理、生物與電腦專家聚會討論,並於次年編輯成The Economy as an Evolving Complex System一書。自此開始將相關的思維推廣。於1996年輯錄的The Economy as an Evolving Complex System II論文輯則是幾乎集中於經濟領域中。其主要的議題是在過去的十年中,使用複雜系統的觀點來看經濟有些什麼助益?其中談到傳統經濟思維與數學工具研究在下列幾項領域中遭到一些困境


分散式互動

在經濟體中的活動主要是由分散的,同質或(可能是)異質性的組成體同時互動所決定的。任一組成體的行動會受到對其他幾位構成體的預期行動所影響,也會受到整體組成體的集合行動所影響。


沒有全面控制者

沒有任何全面性的控制機制可以掌控所有的互動。所有的控制是經由組成體間競爭與協調的機制達成。經濟行動是經由法律機構所監督,分派的角色,轉移的關連,沒有全面性的、可利用所有機會的競爭者。


互相參差的階層式組織

經濟體包括有許多層面的組織與互動。在某一階層的單位例如作為、行動、策略與產品,通常為下一階層的基石。整體組織不僅是階層式,而且包括各種跨越階層的互動、關連、通訊管道。


持續的適應行為

行動、策略與產品隨著單一組成體累積經驗後便修改適應,整體系統也時時調適。


持續創新

新的利基隨時在新市場、新科技、新作為或新機構中產生。佔領新利基的行動本身可能創造新的利基。結果便是持續的、永不停歇的創新。


非均衡動力

由於新利基、新的潛能、新機會時時產生,經濟體並非在任何最佳點或全域的均衡點運作。改善是一直有可能的而且也真正隨時進行的。


John Holland於1987年稱具有以上特性的系統為適應非線性網絡(adaptive nonlinear network)。這些系統時常出現於自然與社會中,例如神經系統、免疫系統、生態系與經濟體。其基本的特性是組成體並不只是單純的針對刺激來反應,組成體還會預估未來。經濟構成體會形成期望值,他們會建立經濟模型來預測未來,並依此決定行動。這些預測模型並不一定是外顯的、協調的或是相互一致的。將經濟體視為是一個複雜適應非線性網路—演化複雜系統—對於經濟學基礎,同時對於如何設定理論問題及如何解答有深厚的影響。

認知學基礎

新古典經濟理論的認知學基礎是單一的,經濟組成體是理性的最佳化者。這表示組成體以統計機率評估未知並隨著新資訊而使用貝氏原理修正預測,從而選擇滿意度期望值最高的行動。在這樣的單一化組成體認知能力情況下,組成體完全相互瞭解並知悉所有共同資訊,對所存在的世界均使用理性期望。相對的,聖太菲學院的方式則顯得多元化。依照現代認知學理論,認知過程並沒有唯一的或主要的。組成體需要在認知上架構自身的問題,也就是說他們必須要弄懂問題的意義並解決問題。而這些都在有限的認知資源下完成。要懂問題的意義,要學習、要適應,組成體必須使用各式各樣的分散式認知過程。組成體將外界資訊轉化成行動的依據是由經驗而來。而這些經驗或認知解釋並不是互無矛盾才能產生有效的行動。因此組成體是活在自我解讀的世界觀中。而這個複雜世界是由其他時時變化的組成體與他們的行動所構成。組成體無法進行一般所認知的最佳化推論,並不是因為受到有限的記憶空間與處理能力,而是無法精確定義所謂的最佳化行動。同時新古典經濟理論中的演繹理性組成體在指出有效的行動時只是邊緣的角色。任何組成體所擁有的相互共同知識,必需由實際的、特定的認知過程依照實際經驗而得,因此,無法輕易假設所謂的共同知識是存在的。


結構基礎

在一般均衡理論分析,組成體並不是直接與其他組成體互動,而是透過間接的機制—市場—來達成互動。不同於博奕理論中組成體直接與所有其他組成體互動,由償賠矩陣得知輸贏多寡。所以其互動是簡單的或者可以說是極端的一對所有的或所有的對所有的。組成體的內部結構更是抽象化,然而由複雜論的角度看,結構是很重要的。首先,以網路為基礎的結構是很重要的。所有的經濟活動都牽涉到組成體間的互動。所以經濟功能是局限於由網路所架構出來的圖樣。這些網路的特色是相當稀疏的連線。接著,經濟活動是由社會角色與社會上支持的程序也就是說經濟組織。再者,經濟單位都具有遞迴的架構,其本身是由其他經濟單位所構成。然而在這樣的一級級組織下,個體與其行動並非是階層式。由於一級組成個體可能是另一級個體的部份,而且在不同級的個體可能會有互動。在不同級的組織的行動的因果關係可能是相反的。一級的組織其行動可以是自主的可是受到其他級個體的行動或行為的樣式所限制。使用聖太菲角度的基礎組織原則是在一級的個體結合形成另一級的個體。


聖太菲人工股市模型(Santa Fe Artificial Stock Market Model)]


[8] W. Brian Arthur, John H. Holland, Blake LeBaron, Richard Palmer, and Paul Tayler, "Asset Pricing under Endogenous Expectations in an Artificial Stock Market" pages 15-44 in W. Brian Arthur, Steven N. Durlauf, and David A. Lane, The Economy as an Evolving Complex System II, Santa Fe Institute Studies in the Sciences of Complexity, Vol. XXVII, Addison-Wesley, 1997.

[9] Norman Ehrentreich, "The Santa Fe Artificial Stock Market Re-Examined: Suggested Corrections" (html), Economics Working Paper Archive at WUSTL, 2002, (pdf ms.,22pp., available for downloading from above html site).

[10] Blake LeBaron, "Agent-Based Computational Finance: Suggested Readings and Early Research" (pdf preprint), Journal of Economic Dynamics and Control 24:5-7 (2000), 679-702. Published article available at Science Direct.

[11]Blake LeBaron, "A Builder's Guide to Agent-Based Financial Markets" (pdf preprint,18pp,207K), Quantitative Finance 1 (2001), 254-261.

[12] Blake LeBaron, "Building the Santa Fe Artificial Stock Market" (pdf preprint,19pp,126K), Working Paper, Brandeis University, June 2002.

LeBaron provides an insider's look at the construction of the Santa Fe Artificial Stock Market model. He considers the many design questions that went into building the model from the perspective of a decade of experience with agent-based financial markets. He also provides an assessment of the model's overall strengths and weaknesses.

[13] Blake LeBaron, "Calibrating an Agent-Based Financial Market" (pdf,44pp), Graduate School of International Economics and Finance, Working Paper, Brandeis University, Revised March 2003.

This paper develops an agent-based computational stock market with market participants who adapt and evolve their behaviors over time. The market model is calibrated to match the variability and growth of dividend payments in U.S. data. The market model generates some features that are remarkably similar to those from actual U.S. data, including the volatility of the dividend process, the persistence in volatility and volume, and fat-tailed return distributions.


[14] Blake LeBaron, W. Brian Arthur, and Richard Palmer, "Time Series Properties of an Artificial Stock Market Model" (pdf preprint,30pp,324K), Journal of Economic Dynamics and Control 23 (1999), 1487-1516.

A rigorous technical discussion of the Santa Fe Artificial Stock Market Model, including implementation details. Anyone interested in the actual implementation of this model should consult this paper in addition to the Arthur et al. (1997) paper cited above.


Economy from the Perspective of Complex Systems (http://www.kzoo.edu/physics/ccss/materials/comecon.pdf)


COMPLEXITY IN ECONOMICS(http://cob.jmu.edu/rosserjb/COMPLEXITY%20IN%20ECONOMICS.doc)


W. Brian Arthur, "Complexity and the Economy,"Science, 2 April 1999, 284,107-109


將金融市場


Multiscaling and non-universality in fluctuations of driven ... (http://www.nd.edu/~networks/Publication%20Categories/Eisler_EurophyLtr(2005).pdf)


Complex Dynamics and Financial Fragility in an Agent Based Model(http://www.ecomod.net/conferences/ecomod2003/ecomod2003_papers/Gallegati.pdf)


[15] W. Brian Arthur, "Complexity in Economic and Financial Markets," Complexity, Volume 1, Number 1, 1995, pp. 2 0-25.

Provides, among other things, a brief summary of the Santa Fe Artificial Stock Market model by Arthur et al. (1997), below.


David F. Batten, "Coevolving Markets" (Chapter 7, pages 209-245), in Discovering Artificial Economics, Westview Press, 2000.


W. M. van den Bergh, K. Boer, A. de Bruin, U. Kaymak, and J. Spronk, "On Intelligent Agent-Based Analysis of Financial Markets" (pdf,9pp,341K), Working Paper, Erasmus University, Rotterdam, 2002.


S.-H. Chen and C.-H. Yeh, "Evolving Traders and the Business School with Genetic Programming: A New Architecture of the Agent-Based Stock Market," Journal of Economic Dynamics and Control 25 (3-4), March 2001, pages 363-393. Article available at Science Direct.


# S.-H. Chen, T. Lux, and M. Marchesi, "Testing for Nonlinear Structure in an Artificial Financial Market," Journal of Economic Behavior and Organization 46 (2001), 327-342. Article available at Science Direct.


# John Duffy, "Learning to Speculate: Experiments with Artificial and Real Agents," Journal of Economic Dynamics and Control 25(3/4), March 2001, pages 295-319. Article available at Science Direct.

This paper employs parallel experiments with real and computational agents to explore issues originally raised by Kiyotaki and Wright in their well-known search model of money (JPE, 1989). The primary issue of interest is how individuals might come to accept or learn to adopt a convention in which the particular commodity functioning as "money" is dominated in rate of return by other assets, in the sense that it has a higher storage cost. The key offsetting factor is anticipations ("speculation") concerning the ease with which the "money" good can be turned over in trade for other goods that agents have a higher desire to consume. The author shows how each type of experiment can contribute to the experimental design and interpretation of results for the other.


# J. Doyne Farmer and John Geanakoplos (eds.), Beyond Equilibrium and Efficiency, 352pp., Oxford University Press, 2005. ISBN: 0-195-15094-5

From the publisher: "This book presents recent thought on market efficiency, using a complex systems approach to move past equilibrium models and quantify the actual efficiency of markets. The older view that markets are perfectly efficient has come under attack from several different directions, including studies of market anomalies, human psychology, bounded rationality, agent-based modeling, and evolutionary game theory. This volume brings together some of the best economists, physicists, and biologists working on quantitative models of complex self-organized behavior relevant to measuring market efficiency, to stimulate new approaches to understanding financial markets."

J. Doyne Farmer is McKinsey Professor at the Santa Fe Institute, and John Geanakoplos is Professor of Economics at Yale University.


# J. Doyne Farmer and Andrew W. Lo, "Frontiers of Finance: Evolution and Efficient Markets" (pdf,7pp,105K), SFI Working Paper, April 1999.


# Jens Grossklags, Carsten Schmidt, and Jonathan Siegel, "Dumb Software Agents on an Experimental Asset Market" (pdf,22pp.), Working Paper, School of Information and Management Systems, UC Berkeley.


# Cars Hommes, "Heterogeneous Agent Models in Economics and Finance", Chapter 8 in Leigh Tesfatsion and Kenneth L. Judd (editors), Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics, Handbooks in Economics Series, North-Holland, Amsterdam, Spring 2006, to appear.

Abstract: This chapter surveys work on dynamic heterogeneous agent models (HAMs) in economics and finance. Emphasis is given to simple models that, at least to some extent, are tractable by analytic methods in combination with computational tools. Most of these models are behavioral models with boundedly rational agents using different heuristics or rule of thumb strategies that may not be perfect, but perform reasonably well. Typically these models are highly nonlinear, e.g. due to evolutionary switching between strategies, and exhibit a wide range of dynamical behavior ranging from a unique stable steady state to complex, chaotic dynamics. Aggregation of simple interactions at the micro level may generate sophisticated structure at the macro level. Simple HAMs can explain important observed stylized facts in financial time series, such as excess volatility, high trading volume, temporary bubbles and trend following, sudden crashes and mean reversion, clustered volatility and fat tails in the returns distribution.


# Paul Johnson, "What I Learned from the Artificial Stock Market" (pdf,20pp,107K), Working Paper, Department of Political Science, University of Kansas, November 5, 2001.

Abstract:This essay describes some of the changes that were incorporated in the ASM-2.2 revision of the code for the Santa Fe Artificial Stock Market model. It also presents some important lessons for agent-based modelers that can be illustrated with the code.


# Deddy P. Koesrindartoto, "Treasury Auctions, Uniform or Discriminatory?: An Agent-Based Approach" (html), Economics Working Paper No. 04013, Department of Economics, Iowa State University, July 2004.

Abstract: This study develops an agent-based computational economics (ACE) framework to explore experimentally how a Treasury should auction its securities. Buyers are modeled as profit seekers capable of submitting strategic bids via reinforcement learning. Two distinct auction pricing rules are considered, uniform and discriminatory. The author shows that these two rules result in systematically different auction outcomes under different treatment conditions for relative capacity and for price volatility in a secondary security market. In particular, which auction pricing rule generates greater Treasury revenues varies systematically with these treatment factor specifications. These findings help to explain why previous Treasury auction studies attempting to determine "the" best Treasury auction pricing rule have reached contradictory conclusions.


# Blake LeBaron, "Agent-Based Computational Finance", Chapter 9 in Leigh Tesfatsion and Kenneth L. Judd (editors), Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics, Handbooks in Economics Series, North-Holland, Amsterdam, Spring 2006, to appear.

Abstract: This chapter surveys research on agent-based models used in finance. It concentrates on models where the use of computational tools is critical for the process of crafting models that give insights into the importance and dynamics of investor heterogeneity in many financial settings.


# T. Lux and M. Marchesi (guest editors), Special Issue on "Heterogeneous Interacting Agents in Financial Markets," Journal of Economic Behavior and Organization 49, No. 1, in press. Article available at Science Direct.


# T. H. Noe, M. J. Rebello, and J. Wang, "Corporate Financing: An Agent-Based Analysis," Journal of Finance, Vol. 58, 943-973, June 2003.


# Nicholas S. P. Tay and Scott C. Linn, "Fuzzy Inductive Reasoning, Expectation Formation, and the Behavior of Security Prices," Journal of Economic Dynamics and Control 25, March 2001, pages 321-361. Article available at Science Direct.


# Leigh Tesfatsion, "Introduction to Financial Markets" (html).


# Leigh Tesfatsion, "Information, Bubbles, and the Efficient Markets Hypothesis" (html).


# Leigh Tesfatsion, "Notes on the Santa Fe Artificial Stock Market Model" (html).


# Edward P. K. Tsang and Serafin Martinez-Jaramillo, Computational Finance (pdf,310K,6pp), Feature Article, IEEE Computational Intelligence Society, August 2004.

This paper briefly outlines the scope and agenda of computational finance research.


# Frank Westerhoff, "Speculative Markets and the Effectiveness of Price Limits", Journal of Economic Dynamics and Control 28 (2003), 493-508. Article available at Science Direct.


"The End of Certainty in Economics," Talk delivered at the conference Einstein Meets Magritte, Free University of Brussels, 1994. Appeared in Einstein Meets Magritte, D. Aerts, J. Broekaert, E. Mathijs, eds. 1999, Kluwer Academic Publishers, Holland.


The Economy as an Evolving Complex System II.

Edited (with S. Durlauf and D. Lane), Addison-Wesley, 1997.

The Economy as an Evolving Complex System II. Proceedings Volume ...( http://meritbbs.unimaas.nl/staff/silverberg/review.pdf)


A Complex System View of why Stock Markets Crash (http://www.newthesis.org/200401/01-200401.pdf)


Why is Economics not a Complex Systems Science? (http://www.econ.iastate.edu/tesfatsi/MacroCAS.Foster.pdf)


Complex Systems Summer Schools 2005 http://www.globalhealthtrust.org/doc/abstracts/WG6/HargadonPAPER.pdf


Agent-based Microsimulation of Economy from A Complexity Perspective(http://www.idi.ntnu.no/~xiaomeng/paper/itbm-13-02.pdf)


Agent-Based Computational Economics_Modelling Economies as Complex Adaptive Systems (http://web.cenet.org.cn/upfile/68883.pdf)


Handbook of Computational Economics Vol. 2 Agent-Based Computational Economics (http://web.cenet.org.cn/upfile/68884.pdf)


Microsimulation of Complex System Dynamics (http://www.ub.uni-koeln.de/ediss/archiv/2001/11v4116.pdf)


Holbrook, Morris B.. 2003. "Adventures in Complexity: An Essay on Dynamic Open Complex Adaptive Systems, Butterfly Effects, Self-Organizing Order, Coevolution, the Ecological Perspective, Fitness Landscapes, Market Spaces, Emergent Beauty at the Edge of Chaos, and All That Jazz." Academy of Marketing Science Review [Online] 2003 (6) Available: http://www.amsreview.org/articles/holbrook06-2003.pdf

(http://www.amsreview.org/articles.htm)

Mandelbrot, BB (1963). "The Variation of Certain Speculative Prices,” Journal of Business, 36:. 394-429.


(http://www.santafe.edu/arthur/Papers/ADLIntro.html)


REVISITING MARKET EFFICIENCY: THE STOCK MARKET AS A COMPLEX ...( http://www.quantuminvesting.net/samples/144maub.pdf)


Computability and Evolutionary Complexity: Markets As Complex ...( http://www.essex.ac.uk/economics/discussion-papers/papers-text/dp574.pdf)

Agents and Complex Systems (http://www.jot.fm/issues/issue_2002_07/column3.pdf)


A GAME PERSPECTIVE TO COMPLEX ADAPTIVE SYSTEMS (http://lib.tkk.fi/Diss/2005/isbn9512277328/isbn9512277328.pdf)


AGENT-BASED GENETIC AND EMERGENT COMPUTATIONAL MODELS OF COMPLEX ...( http://www.public.asu.edu/~kdooley/papers/compmod.PDF)


Darwinism, probability and complexity: market- based ... (http://staff.um.edu.mt/tsam1/publications/Darwinism.pdf)


The Adaptive Markets Hypothesis: Market Efficiency from an ...http://web.mit.edu/alo/www/Papers/JPM2004.pdf


經濟物理學或金融物理學(econophysics)

這是由物理學家所主導的領域,是指綜合使用統計物理,非線性動力學與組成體為基礎的模擬技術研究經濟與金融市場現象的跨領域研究。經濟物理學(econophysics) [] 於1995年時出現在印度加爾各達舉行的複雜系統國際研討會中。在1997年布達佩斯的國際工作坊則以經濟物理學命名。雖然有些物理學家使用phynance來描述這領域,然而為了與biophysics(研究在生物學中的物理現象)和geophysics(研究地質學中的物理)相對應,所以漸漸多人採用經濟物理學來稱呼這些相關研究。


[16] Sanley, H. E.; Afanasyev, V.; Amaral, L. A. N.; Buldyrev, S. V.; Goldberger, A. L.; Havlin, S.; Leschhorn, H.; Maass, P.; Mantegna, R. N.; Peng, C.-K.; Prince, P. A.; Salinger, M. A.; Stanley, M. H. R.; Viswanathan, G. M., Anomalous fluctuations in the dynamics of complex systems: from DNA and physiology to econophysics, Physica A, Volume 224, Issue 1-2, p. 302-321, 1996.

[17] Mantegna, R. N, H.E. Stanley, An introduction to econophysics: correlations and complexity in finance, Cambridge University Press, 2000. (http://assets.cambridge.org/052162/0082/sample/0521620082ws.pdf) (http://assets.cambridge.org/052162/0082/frontmatter/0521620082_frontmatter.pdf)

[18] De Liso, Nicola, and Giovanni Filatrella, Econophysics: The emergence of a new field? 2002. (http://www.dise.unisa.it/PDF/deliso_filatrella.pdf) (http://www.dse.unibo.it/prin/wp/at4_2_2002.pdf)

[19] Bouchaud, J.-P., P. Cizeau, L. Laloux and M. Potters, Mutual attractions: physics and finance, Physics World, January 1999

[20] Amaral, L.A.N., P. Cizeau, P. Gopikrishnan, Y. Liu, M. Meyer, C.-K. Peng, H.E. Stanley, Econophysics: can statistical physics contribute to the science of economics? Computer Physics Communications 121–122 (1999) 145–152 (http://polymer.bu.edu/hes/articles/acglmps99.pdf)

[21] McCauley, J.L., Dynamics of Markets: Econophysics and Finance from a Physicist’s Standpoint, Cambridge University Press, 2004. (http://www.cap.ca/news/books/Dynamics-McCauley-Martin.pdf)

[22] Burda, Z., J. Jurkiewicz, M.A. Nowak . Is Econophysics a Solid Science? Acta Physica Polonica B34 (2003) 87. (http://arxiv.org/pdf/cond-mat/0301096)

[23] Di Matteo, Tiziana, Enrico Scalas, Michele Tumminello, Econophysics: a new tool to investigate financial markets, Bollettino della Comunità Scientifica in Australasia, Sept. 2004. (http://www.scientific.ambitalia.org.au/bollettino/sept04/dimatteo_ing.pdf)

[24] Scalas, Enrico, Five Years of Continuous-time Random Walks in Econophysics, 2005. (http://econwpa.wustl.edu:8089/eps/fin/papers/0501/0501005.pdf)

[25] Vasconcelos, Giovani L., A Guided Walk Down Wall Street: An Introduction to Econophysics , Brazilian Journal of Physics, vol. 34, no. 3B, September, 2004. (http://www.scielo.br/pdf/bjp/v34n3b/a02v343b.pdf)

[26] Econophysics: statistical physics of interacting agents (http://www.fzu.cz/departments/theory/seminars/presentations/sem-present-031127.pdf) (http://members.jcom.home.ne.jp/ephys/Econophysics%20Stauffer.pdf)

[27] Gordon M.B., Nadal J.P., Phan D., Statistical Mechanics Approaches in Economics: Suggested Reading and Interpretations, (http://www.cenecc.ens.fr/EcoCog/Livre/Drafts/MBGJPNDPv5.pdf)

[28] Farmer, J. Doyne, Martin Shubik, and Eric Smith, Economics: the next physical science? (www.santafe.edu/research/publications/workingpapers/05-06-027.pdf) (http://cowles.econ.yale.edu/P/cd/d15a/d1520.pdf)

[29] Yakovenko, Victor M., Research in Econophysics, 2003. (http://www2.physics.umd.edu/~yakovenk/papers/condmat-0302270.pdf)

[30] Plerou, Vasiliki, Parameswaran Gopikrishnan, Bernd Rosenow, Luis A.N. Amaral, H. Eugene Stanley, Econophysics: Financial Time Series From a Statistical Physics Point of View, (http://polymer.bu.edu/~amaral/Papers/physa00a.pdf)

(http://members.jcom.home.ne.jp/ephys/)

(http://iapetus.phy.umist.ac.uk/Teaching/LitStudies/Essays/Econophysics.html)


一方面由於在金融界使用數位技術進行交易與儲存資料漸漸普遍,且每日產生的金融資料龐大而且可以十分容易取得。例如Trades and Quotes Database: a monthly CD-ROM with every transaction at NYSE, AMEX, and NASDAQ。另一方面一些統計物理學家認為使用統計力學方法可以由這些資料中找到經濟學家所沒注意到的規律性且或許可由物理定律提供一些可能解釋。

幾個時常見到的議題:財富與收入分佈,價格波動,買賣簿,探討量尺現象,臨界行為,冪次律分佈與寡勝博奕。


http://www.bwl.uni-kiel.de/vwlinstitute/gwif/teaching/handouts/tdf/Tutorial%20Fat%20Tails.pdf


Essays on Asset Return Distributions http://www.google.com.tw/url?sa=t&ct=res&cd=212&url=http%3A//www.int9.com/download/isbn9512262541.pdf&ei=TgH4QuXyEInqswGbqqj0DQ


價格波動是廣為研究的議題。


http://www.physics.ubc.ca/~jinshanw/project/ecophys/review/review.html


The Statistical Physics of financial markets http://iapetus.phy.umist.ac.uk/Teaching/LitStudies/Essays/Econophysics.html


假設pt 表示某一金融商品在時間t時的價格, pt是非靜駐式序列(non-stationary)

也就是說,[pt] 是與時間t的函數。序列


價格報酬(price returns)
1   2   3   4   5   6   7

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