A theory of fluctuations in stock prices

Physica A: Statistical Mechanics and its Applications

Volumn 363, Issue 2, 2006, Pages 383-392

  Alejandro Quiñones, Ángel L ^a   Bassler, Kevin E ^a   Field, Michael ^a   McCauley, Joseph L ^a   Nicol, Matthew ^a   Timofeyev, Ilya ^a   Török, Andrew ^a   Gunaratne, Gemunu H ^a,b  

^a University of Houston   (United States)

^b INSTITUTE OF FUNDAMENTAL STUDIES   (Sri Lanka)

Author keywords

Diffusion; Fat tailed distributions; Levy flights; Price returns; Random walk

Indexed keywords

COMPUTER SIMULATION; COST BENEFIT ANALYSIS; DIFFUSION; MARKETING; MARKOV PROCESSES;

FAT-TAILED DISTRIBUTIONS; LEVY FLIGHTS; PRICE RETURNS; RANDOM WALK;

INDUSTRIAL ECONOMICS;

EID: 33644857532     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2005.08.037     Document Type: Article

References (33)

1. B. Castaing, G. Gunaratne, F. Heslot, L. Kadanoff, A. Libchaber, S. Thomae, X.-Z. Wu, S. Zaleski, and G. Zanetti J. Fluid Mech. 204 1989 1
2. S. Havlin, and D. Avraham Adv. Phy. 36 1987 695
3. J.W. Hans, and K.W. Kehr Phys. Rep. 150 1981 263
4. M.M. Dacorogna, R. Gencay, U. Müller, R.B. Olsen, and O.V. Pictet An Introduction to High-Frequency Finance 2001 Academic Press San Diego
5. R.N. Mantegna, and H.E. Stanley Nature 376 1995 46
6. R.N. Mantegna, and H.E. Stanley Nature 383 1996 587
7. W. Feller An Introduction to Probability Theory 1957 Wiley New York
8. J.P. Bouchaud, and A. Georges Phys. Rep. 195 1990 127
9. J. Klafter, M.F. Shlesinger, and G. Zumofen Phys. Today 1 February 1996 33
10. N.G. Van Kampen Stochastic Processes in Physics and Chemistry 1981 North-Holland Amsterdam
11. R. Friedrich, J. Peinke, and Ch. Renner Phys. Rev. Lett. 84 2000 5224
12. A. Arneodo, J.P. Bouchaud, R. Cont, J.F. Muzy, M. Potters, D. Sornette, cond-mat/9607120 at lanl.arXiv.org.
13. M.F.M. Osborne P. Cooter The Random Character of Stock Market Prices 1964 MIT Press Cambridge, MA
14. B. Mandlebrot J. Bus. 36 1963 392
15. P. Gopikrishnan, V. Plerou, L.A. Nunes Amaral, M. Meyer, and H.E. Stanley Phys. Rev. E 60 1999 5305
16. V. Plerou, P. Gopikrishnan, L.A. Nunes Amaral, M. Meyer, and H.E. Stanley Phys. Rev. E 60 1999 6519
17. K. Lee, J. Lee, cond-mat/0407418 at lanl.arXiv.org.
18. H.F. Coronel-Brizio, C.R. de la Cruz-Laso, A.R. Hernandez-Montoya, cond-mat/0303568 lanl.arXiv.org.
19. J.P. Bouchaud, and M. Potters Theory of Financial Risks 2000 Cambridge University Press Cambridge
20. J.L. McCauley, and G.H. Gunaratne Physica A 329 2003 178
21. J.L. McCauley Dynamics of Markets: Econophysics and Finance 2004 Cambridge University Press Cambridge
22. S. Chandrasekar Rev. Mod. Phys. 15 1943 1
23. A.D. Fokker Ann. d. Physik 43 1914 812
24. M. Planck, Sitzungsber, Preuss. Akad. (1917) 324.
25. Possibilities that include anomalous diffusion have been considered in, for example, Refs. [5] and [25].
26. Fokker-Planck equations with variables R and D have been used previously to describe dynamics of financial markets, see for example S. Maslov, Y.-C. Zhang, Physica A 262 (1999) 232
27. and L. Ramusson, E. Aurell, cs.NI.0102011 at arXiv. Non-linear Fokker-Planck equations have also been proposed, see Ref. [35].
28. R. Cont, M. Potters, and J.P. Bouchaud Scaling in stock market data: stable laws and beyond B. Dubrulle F. Graner D. Sornette Scale Invariance and Beyond, Proceedings of the CNRS Workshop on Scale Invariance 1997 Springer Berlin
29. P. Levy Theorie de l'Addition des Variables Aleatoires 1937 Gauthier-Villars Paris
30. R. Weron Int. J. Mod. Phys. C 12 2001 209
31. P.D. Praetz J. Bus. 45 1972 49
32. R.C. Blattberg, and N.J. Gonedes J. Bus. 47 1974 244
33. R.N. Mantegna, and H.E. Stanley An Introduction to Econophysics 2000 Cambridge University Press Cambridge