Applications of statistical physics in finance and economics

Handbook of Research on Complexity

Volumn , Issue , 2009, Pages 213-258

  Lux, Thomas ^a  

^a KIEL INSTITUTE FOR THE WORLD ECONOMY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84881711346     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (158)

1. Amaral, L.A.N., S.V. Buldyrev, S. Havlin, P. Maass, M.A. Salinger, H.E. Stanley and M.H.R. Stanley (1997), "Scaling behavior in economics: The problem of quantifying company growth", Physica A, 244(1), 1-24.
2. Angle, J. (1986), "The surplus theory of social stratification and the size distribution of personal wealth", Social Forces, 65(2), 293-326.
3. Angle, J. (1993), "Deriving the size distribution of personal wealth from 'The rich get richer, the poor get poorer'", Journal of Mathematical Sociology, 18, 27-46.
4. Angle, J. (1996), "How the gamma law of income distribution appears invariant under aggregation", Journal of Mathematical Sociology, 31, 325-58.
5. Angle, J. (2006), "The inequality process as a wealth maximizing process", Physica A, 367, 388-414.
6. Anglin, P.M. (2005), "Econophysics of wealth distribution: A comment", in A. Chatterjee et al. (eds), Econophysics of Wealth Distribution, Milan: Springer-Verlag Italia, pp. 229-38.
7. Aoki, M. (1996), New Approaches to Macroeconomic Modeling: Evolutionary Stochastic Dynamics, Multiple Equilibria, and Externalities as Field Effects, Cambridge, MA: Cambridge University Press.
8. Aoki, M. (2002), Modeling Aggregate Behavior and Fluctuations in Economics, Cambridge, MA: Cambridge University Press.
9. Aoki, M. and H. Yoshikawa (2007), A Stochastic Approach to Macroeconomics and Financial Markets, Cambridge, MA: Cambridge University Press.
10. Arifovic, J. (1996), "The behavior of the exchange rate in the genetic algorithm and experimental economies", Journal of Political Economy, 104(3), 510-41.
11. Ausloos, M. and N. Vandewalle (1998), "Multi-affine analysis of typical currency exchange rates", European Physical Journal B, 4(2), 257-61.
12. Axtell, R.L. (1999), "The emergence of firms in a population of agents: Local increasing returns, unstable Nash equilibria and power law size distribution", Brookings Institution, Center for Social and Economic Dynamics, Working Paper.
13. Axtell, R.L. (2001), "Zipf distribution of U.S. firm sizes", Science, 293(5536), 1818-20.
14. Bacry, E., A. Kozhemyak and J.-F. Muzy (2008), "Continuous cascade models for asset returns", Journal of Economic Dynamics and Control, 32(1), 156-99.
15. Baillie, R.T., T. Bollerslev and H. Mikkelsen (1996), "Fractionally integrated generalized autoregressive conditional heteroskedasticity", Journal of Econometrics, 74(1), 3-30.
16. Bak, P., M. Paczuski and M. Shubik (1997), "Price variations in a stock market with many agents", Physica A, 246, 430-53.
17. Bartolozzi, M. and A.W. Thomas (2004), "Stochastic cellular automata model for stock market dynamics", Physical Review E, E69(4), 046112.
18. Bollerslev, T. (1986), "A generalized autoregressive conditional heteroskedasticity", Journal of Econometrics, 31(3), 307-27.
19. Bouchaud, J.-P. and M. Mézard (2000), "Wealth condensation in a simple model of economy", Physica A, 282, 536-45.
20. Bouchaud, J.-P. and M. Potters (2000), Theory of Financial Risks: From Statistical Physics to Risk Management, Cambridge, UK: Cambridge University Press.
21. Bouchaud, J.-P., M. Potters and M. Mézard (2002), "Statistical properties of stock order books: Empirical results and models", Quantitative Finance, 2(4), 251.
22. Breidt, F., N. Crato and P. de Lima (1998), "On the detection and estimation of long memory in stochastic volatility", Journal of Econometrics, 83(1-2), 325-48.
23. Buchanan, M. (2002), "Wealth happens", Harvard Business Review, 80(4), 49-54.
24. Calvet, L.E. and A. Fisher (2001), "Forecasting multifractal volatility", Journal of Econometrics, 105(1), 27-58.
25. Calvet, L.E. and A. Fisher (2002), "Multifractality in asset returns: Theory and evidence", The Review of Economics and Statistics, 84(3), 381-406.
26. Calvet, L.E. and A. Fisher (2004), "How to forecast long-run volatility: Regime switching and the estimation of multifractal processes", Journal of Financial Econometrics, 2(1), 49-83.
27. Calvet, L.E., A. Fisher and S.B. Thompson (2006), "Volatility comovement: A multifrequency approach", Journal of Econometrics, 131(1-2), 179-215.
28. Calvet, L.E., B. Mandelbrot and A. Fisher (1997), "Large deviations and the distribution of price changes", Mimeo: Cowles Foundation for Research in Economics.
29. Canning, D., L.A.N. Amaral, Y. Lee, M. Meyer and H.E. Stanley (1998), "A power law for scaling the volatility of GDP growth rates with country size", Economics Letters, 60(3), 335-41.
30. Castaldi, C. and M. Milakovic (2007), "Turnover activity in wealth portfolios", Journal of Economic Behavior and Organization, 63(3), 537-52.
31. Castañeda, A., J. Díaz-Giménez and J.-V. Ríos-Rull (2003), "Accounting for the US earnings and wealth inequality", The Journal of Political Economy, 111(4), 818-57.
32. Castiglione, F. and D. Stauffer (2001), "Multi-scaling in the Cont-Bouchaud microscopic stockmarket model", Physica A, 300(3), 531-8.
33. Chakraborti, A. and B. Chakrabarti (2000), "Statistical mechanics of money: How saving propensities affects its distribution", European Physical Journal B, 17, 167-70.
34. Champernowne, D.G. (1953), "A model of income distribution", The Economic Journal, 63, 318-51.
35. Chang, G. and J. Feigenbaum (2006), "A Bayesian analysis of log-periodic precursors to financial crashes", Quantitative Finance, 6(1), 15-36.
36. Chatterjee, A., B. Chakrabarti and S.S. Manna (2003), "Money in gas-like markets: Gibbs and Pareto laws", Physica Scripta, 106, 36-38.
37. Chen, S.-H., T. Lux and M. Marchesi (2001), "Testing for non-linear structure in an artificial market", Journal of Economic Behavior and Organization, 46(3), 327-42.
38. Chen, N., R. Roll and S.A. Ross (1986), "Economic forces and the stock market", Journal of Business, 59(3), 383-403.
39. Chiarella, C. and G. Iori (2002), "A simulation analysis of the microstructure of double auction markets", Quantitative Finance, 2(5), 346-53.
40. Cioffi, C. (2008) (ed.), Power Laws in the Social Sciences: Discovering Complexity and Nonequilibrium Dynamics in Social Universe, in preparation.
41. Cont, R. and J.-P. Bouchaud (2000), "Herd behavior and aggregate fluctuations in financial markets", Macroeconomic Dynamics, 4(2), 170-96.
42. Cross, R. (ed.) (1988), Hysteresis and the Natural Rate Hypothesis, Oxford: Blackwell.
43. Dacorogna, M., R. Gencay, U. Muller, R. Olsen and O. Pictet (2001), An Introduction to High-frequency Finance, San Diego: Academic Press.
44. Daniels, M.G., J.D. Farmer, L. Gillemot, G.Iori and E. Smith (2003), "Quantitative model of price diffusion and market friction based on trading as a mechanistic random process", Physical Review Letters, 90(10), 108102(4).
45. Delli Gatti, D., M. Gallegati, G. Giuleoni and A. Palestrini (2003), "Financial fragility, patterns of firms' entry and exit and aggregate dynamics", Journal of Economic Behavior and Organization, 51(1), 79-97.
46. Diamond, D.W. (1982), "Aggregate demand management in search equlibrium", Journal of Political Economy, 90(5), 881-94.
47. Ding, Z., R. Engle and C. Granger (1993), "A long memory property of stock market returns and a new model", Journal of Empirical Finance, 1(1), 83-106.
48. Dragulescu, A.A. and V.M. Yakovenko (2000), "Statistical mechanics of money, income, and wealth", European Physical Journal B, 17(4), 723-9.
49. Eguiluz V.M. and M.G. Zimmermann (2000), "Transmission of information and herd behavior: An application to financial markets", Physical Review Letters, 85(26), 5659-62.
50. Eisler, Z. and J. Kertész (2005), "Size matters: Some stylized facts of the stock market revisited", European Physical Journal B, 51(1), 145-54.
51. Engle, R. (1983), "Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation", Econometrica, 50(4), 987-1008.
52. Epstein, J.M. and R.L. Axtell (1996), Growing Artificial Societies: Social Science from the Bottom Up, Cambridge, MA: MIT Press.
53. Fama, E. (1963), "Mandelbrot and the stable Paretian hypothesis", Journal of Business, 36(4), 420-29.
54. Farmer, J.D. and F. Lillo (2004), "On the origin of power law tails in price fluctuations", Quantitative Finance, 4(1), C7-C11.
55. Farmer, J.D. and I.I. Zovko (2002), "The power of patience: A behavioral regularity in limit order placement", Quantitative Finance, 2(5), 387-92.
56. Feigenbaum, J.A. (2001a), "A statistical analysis of log-periodic precursors to financial crashes", Quantitative Finance, 1(3), 346-60.
57. Feigenbaum, J.A. (2001b), "More on a statistical analysis of log-periodic precursors to financial crashes", Quantitative Finance, 1(5), 527-32.
58. Fisher, A., L.E. Calvet and B. Mandelbrot (1997), "Multifractality of Deutschemark/US Dollar exchange rates", Mimeo: Cowles Foundation for Research in Economics.
59. Focardi, S., S. Cincotti and M. Marchesi (2002), "Self-organization and market crashes", Journal of Economic Behavior and Organization, 49(2), 241-67.
60. Fujiwara, T., W. Souma, H. Aoyama, T. Kaizaji and M. Aoki (2003), "Growth and fluctuations of personal income", Physica A, 321(3-4), 598-604.
61. Gabaix, X. (1999), "Zipf's law for cities: An explanation", The Quarterly Journal of Economics, 114(3), 739-767.
62. Gabaix, X., P. Gopikrishnan, V. Plerou and H.E. Stanley (2003), "A theory of power-law distributions in financial market fluctuations", Nature, 423, 267-70.
63. Galluccio, S., J.-P. Bouchaud and M. Potters (1998), "Rational decisions, random matrices and spin glasses", Physica A, 259, 449-56.
64. Ghashghaie, S., W. Breymann, D. Peinke, P. Talkner and Y. Dodge (1996), "Turbulent cascades in foreign exchange markets", Nature, 381, 767-70.
65. Giardina, I. and J.-P. Bouchaud (2003), "Bubbles, crashes and intermittency in agent based market models", European Physical Journal B, 31(3), 421-37.
66. Gibrat, R. (1931), Le Inégalités Economiques, Paris: Librairie du Recueil.
67. Gode, D.K. and S. Sunder (1993), "Allocative efficiency of markets with zero-intelligence traders: Market as a partial substitute for individual rationality", Journal of Political Economy, 101(1), 119-37.
68. Gopikrishnan, P., M. Meyer, L.A.N. Amaral and H.E. Stanley (1998), "Inverse cubic law for the probability distribution of stock price variations", European Journal of Physics B, 3, 139-40.
69. Gopikrishnan P., V. Plerou, X. Gabaix, L.A.N. Amaral and H.E. Stanley (2001), "Price fluctuations, market activity and trading volume", Quantitative Finance, 1, 262-70.
70. Hayes, B. (2002), "Follow the money", American Scientist, 90(5), 400-405.
71. Huggett, M. (1996), "Wealth distribution in life-cycle economies", Journal of Monetary Economics, 38(3), 469-94.
72. Iori, G. (2002), "A micro-simulation of traders' activity in the stock market: The role of heterogeneity of agents' interactions and trade-friction", Journal of Economic Behavior and Organization, 49(2), 269-85.
73. Jansen, D. and C. de Vries (1991), "On the frequency of large stock returns: Putting booms and busts into perspective", The Review of Economics and Statistics, 73(1), 18-24.
74. Johansen, A. and D. Sornette (1999a), "Financial 'anti-bubbles': Log-periodicity in gold and Nikkei collapses", International Journal of Modern Physics C, 10(7), 563-75.
75. Johansen, A. and D. Sornette (1999b), "Predicting financial crashes using discrete scale invariance", Journal of Risk, 1(4), 5-32.
76. Johansen, A. and D. Sornette (2001a), "Finite-time singularity in the dynamics of the world population and economic indices", Physica A, 294(3-4), 405-502.
77. Johansen, A. and D. Sornette (2001b), "Bubbles and anti-bubbles in Latin-American, Asian and Western stock markets: An empirical study", International Journal of Theoretical and Applied Finance, 4(6), 853-920.
78. Kareken, J. and N. Wallace (1981), "On the indeterminacy of equilibrium exchange rates", The Quarterly Journal of Economics, 96, 207-22.
79. Kim, G. and H. Markowitz (1989), "Investment rules, margins, and market volatility", Journal of Portfolio Management, 16(1), 45-52.
80. Kirman, A. (1991), "Epidemics of opinion and speculative bubbles in financial markets", in M. Taylor (ed.), Money and Financial Markets, London: Macmillan.
81. Kirman, A. (1992), "Whom or what does the representative agent represent?", Journal of Economic Perspectives, 6(2), 117-36.
82. Kirman, A. (1993), "Ants, rationality, and recruitment", The Quarterly Journal of Economics, 108(1), 137-56.
83. Knell, M. and H. Stix (2003), "Three decades of money demand studies: Similarities and differences", Applied Economics, 38(7), 805-18.
84. Krusell, P. and A. Smith Jr. (1998), "Income and wealth heterogeneity in the macroeconomy", Journal of Political Economy, 106(5), 867-96.
85. Kullmann, L., J. Kertész and K. Kaski (2002), "Time-dependent cross-correlations between different stock returns: A directed network of influence", Physical Review E, 66(2), 026125.
86. Laloux, L., P. Cizeau, M. Potters and J.-P. Bouchaud (2000), "Random matrix theory and financial correlations", International Journal of Theoretical and Applied Finance, 3(3), 391-7.
87. Levy, M. and S. Solomon (1997), "New evidence for the power-law distribution of wealth", Physica A, 242(1), 90-94.
88. Levy, H., M. Levy and S. Solomon (1994), "A microscopic model of the stock market: Cycles, booms, and crashes", Economics Letters, 45(1), 103-11.
89. Levy, H., M. Levy and S. Solomon (1995), "Simulations of the stock market: The effects of microscopic diversity", Journal de Physique I, 5(8), 1087-107.
90. Levy, H., M. Levy and S. Solomon (2000), Microscopic Simulation of Financial Markets: From Investor Behavior to Market Phenomena, San Diego: Academic Press.
91. Liu, Y., P. Cizeau, M. Meyer, C.-K. Peng and G. Stanley (1997), "Correlations in economic time series", Physica A, 245, 437-40.
92. Lobato, I.N. and C. Valasco (2000), "Long memory in stock market trading volume", Journal of Business and Economic Statistics, 18(4), 410-27.
93. Lux, T. (1995), "Herd behavior, bubbles and crashes", The Economic Journal, 105(431), 881-96.
94. Lux, T. (1996), "The stable Paretian hypothesis and the frequency of large returns: An examination of major German stocks", Applied Financial Economics, 6(6), 463-75.
95. Lux, T. (1997), "Time variation of second moments from a noise trader/infection model", Journal of Economic Dynamics and Control, 22(1), 1-38.
96. Lux, T. (1998), "The socio-economic dynamics of speculative markets: Interacting agents, chaos, and the fat tails of return distributions", Journal of Economic Behavior and Organization, 33(2), 143-65.
97. Lux, T. (2005a), "Financial power laws: Empirical evidence, models, and mechanisms", Working Paper, University of Kiel.
98. Lux, T. (2005b), "Emergent statistical wealth distributions in simple monetary exchange models: A critical review", in A. Chatterjee et al. (eds), Econophysics of Wealth Distributions, Milan: Springer-Verlag Italia, pp. 51-90.
99. Lux, T. (2008), "The Markov-switching multifractal model of asset returns: GMM estimation and linear forecasting of volatility", Journal of Business and Economics Statistics, 26(3), 194-210.
100. Lux, T. and M. Marchesi (1999), "Scaling and criticality in a stochastic multi-agent model of a financial market", Nature, 397, 498-500.
101. Lux, T. and M. Marchesi (2000), "Volatility clustering in financial markets: A microsimulation of interacting agents", International Journal of Theoretical and Applied Finance, 3(4), 675-702.
102. Lux, T. and S. Schornstein (2005), "Genetic algorithms as an explanation of stylized facts of foreign exchange markets", Journal of Mathematical Economics, 41, 169-96.
103. McCauley, J. (2006), "Response to 'worrying trends in econophysics'", Physica A, 371(2), 601-9.
104. Mandelbrot, B. (1961), "Stable Paretian random functions and the multiplicative variation of income" Econometrica, 29(4), 517-43.
105. Mandelbrot, B. (1963), "The variation of certain speculative prices", Journal of Business, 26(4), 394-419.
106. Mandelbrot, B., A. Fisher and L.E. Calvet (1997), "A multifractal model of asset returns", Mimeo: Cowles Foundation for Research in Economics.
107. Mantegna, R.H. (1991), "Levy walks and enhanced diffusion in Milan stock exchange", Physica A, 179, 232-42.
108. Mantegna, R. (1999), "Hierarchical structure in financial markets", European Physical Journal B, 11, 193-7.
109. Mantegna, R.H. and H.E. Stanley (1995), "Scaling behaviour in the dynamics of an economic index", Nature, 376, 46-9.
110. Mantegna, R.H. and H.E. Stanley (1996), "Turbulence and financial markets", Nature, 383, 587-8.
111. Markowitz, H. (1952) "The utility of wealth", The Journal of Political Economy, 60(2), 151-8.
112. Maslov, S. (2000), "Simple model of a limit order-driven market", Physica A, 278(3), 571-8.
113. Matia, K. and K. Yamasaki (2005), "Statistical properties of demand fluctuations in the financial markets", Quantitative Finance, 5(6), 513-17.
114. Nitsch, V. (2005), "Zipf zipped", Journal of Urban Economics, 57(1), 86-100.
115. Noh, J.D. (2000), "Model for correlations in stock markets", Physical Review E, 61(5), 5981-2.
116. O'Hara, M. (1995), Market Microstructure Theory, Oxford: Blackwell Business.
117. Okuayama, R., M. Takayasu and H. Takayasu (1999), "Zipf's law in income distribution of companies", Physica A, 269(1), 125-31.
118. Onnela, J.-P., A. Chakraborti, K. Kaski, J. Kertesz and A.Kanto (2003), "Dynamics of market correlations: Taxonomy and portfolio analysis", Physical Review E, 68(5), 056110.
119. Pareto, V. (1897), Cours d'Economie Politique, Lausanne: F. Rouge.
120. Peng, C.K., S.V. Buldyrev, S. Havlin, M. Simons, H.E. Stanley and A.L. Goldberger (1994), "Mosaic organization of DNA nucleotides", Physical Review E, 49, 1685-9.
121. Plerou, V., P. Gopikrishnan and H.E. Stanley (2003), "Two-phase behavior of financial markets", Nature, 421, 130.
122. Plerou, V., P. Gopikrishnan, B. Rosenow, L.A.N. Amaral and H.E. Stanley (2000), "A random matrix theory approach to financial cross-correlations", Physica A, 287, 374-82.
123. Quandt, R.E. (1966), "On the size distribution of firms", American Economic Review, 61(3), 416-32.
124. Ramsey, J. (1996), "On the existence of macro variables and macro relationships", Journal of Economic Behavior and Organization, 30(3), 275-99.
125. Rosenow, B. (2008), "Determining the optimal dimensionality of multivariate volatility models with tools from random matrix theory", Journal of Economic Dynamics and Control, 32(1), 279-302.
126. Sato, A.-H. and H. Takayasu (1998), "Dynamical models of stock market exchanges: From microscopic determinism to macroscopic randomness", Physica A, 250, 231-52.
127. Silva, A.C. and V.M. Yakovenko (2005), "Temporal evolution of the 'thermal' and 'superthermal' income classes in the USA during1983-2001", Europhysics Letters, 69(2), 304-10.
128. Silver, J., E. Slud and K. Takamoto (2002), "Statistical equilibrium wealth distributions in an exchange economy with stochastic preferences", Journal of Economic Theory, 106(2), 417-35.
129. Sinha, S. (2005), "The rich are different! Pareto law from asymmetric interactions in asset exchange models", in A. Chatterjee et al. (eds), Econophysics of Wealth Distributions, Milan: Springer-Verlag Italia, pp. 177-83.
130. Slanina, F. (2001), "Mean-field approximation for a limit order-driven market model", Physical Review E, 64(5), 056136.
131. Smith, E., J.D. Farmer, L. Gillemot and S. Krishnamurthy (2002), "Statistical theory of the continuous double auction", Quantitative Finance, 3(6) 481-514.
132. Sornette, D. and A. Johansen (1997), "Large financial crashes", Physica A, 245(3-4), 411-22.
133. Sornette, D. and W.-X. Zhou (2002), "The US 2000-2002 market descent: How much longer and deeper?", Quantitative Finance, 2(6), 468-81.
134. Sornette, D., A. Johansen and J.-P. Bouchaud (1996), "Stock market crashes, precursors and replicas", Journal de Physique I, 6(1), 167-75.
135. Stanley, M.H.R., S.V. Buldyrev, S. Havlin, R.N. Mantegna, M.A. Salinger and H.E. Stanley (1995), "Zipf plots and the size distribution of firms" Economic Letters, 49(4) 453-57.
136. Stanley, M.H.R., L.A.N. Amaral, S.V. Buldyrev, S. Havlin, H. Leschhorn, P. Maass, M.A. Salinger and H.E. Stanley (1996a), "Can statistical physics contribute to the science of economics?", Fractals, 4(3), 415-25.
137. Stanley, M.H.R., L.A.N. Amaral, S.V. Buldyrev, S. Havlin, H. Leschhorn, P. Maass, M.A. Salinger and H.E. Stanley (1996b), "Scaling behavior in the growth of companies", Nature, 379, 804-6.
138. Stauffer, D. (2002), "How to get rich with Sornette and Zhou", Quantitive Finance, 2(6), 408.
139. Stauffer, D. and T. Penna (1998), "Crossover in the Cont-Bouchaud percolation model for market fluctuations", Physica A, 256, 284-90.
140. Stauffer, D. and D. Sornette (1999), "Self-organized percolation model for stockmarket fluctuations", Physica A, 271(3-4), 496-506.
141. Stauffer, D., P. de Oliveira and A. Bernardes (1999), "Monte-Carlo simulation of volatility clustering in a market model with herding", International Journal of Theoretical and Applied Finance, 2(1), 83-94.
142. Steindl, J. (1965), Random Processes and the Growth of Firms: A Study of the Pareto Law, London: Griffin.
143. Stigler, G. (1964), "Public regulation of the securities markets", Journal of Business, 37(2), 117-42.
144. Sullivan, R., H. White and B. Golomb (2001), "Dangers of data mining: The case of calendar effects in stock returns", Journal of Econometrics, 105(1), 249-86.
145. Sutton, J. (2002), "The variance of firm growth rates: The scaling puzzle", Physica A, 312(3), 577-90.
146. Takayasu, H., H. Miura, T. Hirabayashi and K. Hamada (1992), "Statistical properties of deterministic threshold elements - the case of market price", Physica A, 184, 127-34.
147. Tang, L.H. and G.-S. Tian (1999), "Reaction-diffusion-branching models of stock price fluctuations", Physica A, 264(3), 543-50.
148. Vandewalle, N. and M. Ausloos (1997), "Coherent and random sequences in financial fluctuations", Physica A, 246, 454-9.
149. Vandewalle, N. and M. Ausloos (1998), "How the financial crash of October 1997 could have been predicted", The European Physical Journal, 4(2), 139-41.
150. Vassilicos, J.C. (1995), "Turbulence and intermittency", Nature, 374, 408-9.
151. Vassilicos, J.C., A. Demos and F. Tata (1993), "No evidence of chaos but some evidence of multifractals in the foreign exchange and the stock market", in A.J. Crilly, R.A. Earnshaw and H. Jones (eds), Applications of Fractals and Chaos, Berlin: Springer.
152. Voit, J. (2005), Statistical Mechanics of Financial Markets, 3rd edn, Berlin: Springer.
153. Whittle, P. and H.O.A. Wold (1957), "A model explaining the Pareto distribution of wealth", Econometrica, 25(4), 591-5.
154. Wright, I. (2005), "The social architecture of capitalism", Physica A, 346(3-4), 589-620.
155. Yakovenko, V. and C. Silva (2005), "Two-class structure of income distribution in the U.S.A.: Exponential bulk and power-law tail", in A. Chatterjee, S. Yarlagadda and B. Chakraborti (eds), Econophysics of Wealth Distribution, Berlin, Springer.
156. Zhang, Y.-C. (1999), "Towards a theory of marginally efficient markets", Physica A, 269(1), 30-44.
157. Zhou, W.-X. and D. Sornette (2003), "Evidence of a worldwide stock market log-periodic anti-bubble since mid-2000", Physica A, 330(3-4), 543-83.
158. Zschischang, E. and T. Lux (2001), "Some new results on the Levy, Levy and Solomon microscopic stock market model", Physica A, 29, 563-73.