On the emergence of a generalised Gamma distribution. Application to traded volume in financial markets

Europhysics Letters

Volumn 71, Issue 3, 2005, Pages 339-345

  Queirós, S M Duarte ^a  

^a CENTRO BRASILEIRO DE PESQUISAS FÍSICAS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23444442382     PISSN: 02955075     EISSN: None     Source Type: Journal    
DOI: 10.1209/epl/i2005-10109-0     Document Type: Article

References (47)

1. BOUCHAUD J.-P. and POTTERS M., Theory of Financial Risks: From Statistical Physics to Risk Management (Cambridge University Press, Cambridge) 2000;
2. DOYNE FARMER J., Int. J. Appl. Finance, 3 (2000) 311;
3. VOIT J., The Statistical Mechanics of Financial Markets (Texts and Monographs in Physics) (Springer-Verlag, Berlin) 2003.
4. MANTEGNA R. N. and STANLEY H. E., An Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge University Press, Cambridge) 1999.
5. GELL-MANN M. and TSALLIS C. (Editors), Nonextensive Entropy - Interdisciplinary Applications (Oxford University Press, New York) 2004.
6. BAK P., How Nature Works: The Science of Self Organized Criticality (Copernicus, Oxford) 1997.
7. MANTEGNA R. N. and STANLEY H. E., Nature, 376 (1995) 46;
8. PLEROU V., GOPIKRISHNAN P., AMARAL L. A. N., MEYER M. and STANLEY H. E., Phys. Rev. E, 60 (1999) 6519;
9. AUSLOOS M. and IVANOVA K., Phys. Rev. E, 68 (2003) 046122;
10. DUARTE QUEIRÓS S. M., Physica A, 344 (2004) 279.
11. DRAGULESCU A. A. and YAKOVENKO V. M., Quantit. Finance, 2 (2002) 443;
12. SILVA A. C., PRANGE R. E. and YAKOVENKO V. M., Physica A, 344 (2004) 227.
13. OSORIO R., BORLAND L. and TSALLIS C., in Nonextensive Entropy - Interdisciplinary Applications, edited by GELL-MANN M. and TSALLIS C. (Oxford University Press, New York) 2004, p. 321.
14. GHASHGHAIE S., BREYMANN W., PEINKE J., TALKNER P. and DODGE Y., Nature, 381 (1996) 767;
15. ARNÉODO A., MUZY J.-F. and SORNETTE D., Eur. Phys. J. B, 2 (1998) 277.
16. DING Z., GRANGER C. W. J. and ENGLE R. F., J. Empir. Finance, 1 (1993) 83.
17. POTTERS M., CONT R. and BOUCHAUD J. P., Europhys. Lett., 41 (1998) 239.
18. PLEROU V., GOPIKRISHNAN P., GABAIX X. and STANLEY H. E., Phys. Rev. E, 66 (2002) 027104;
19. DOYNE FARMER J., GILLEMOT L., LILLO F., MIKE S. and SEN A., Quantit. Finance, 4 (2004) 383.
20. STANLEY H. E., AMARAL L. A. N., BULDYREV S. V., GOPIKRISHNAN P., PLEROU V. and SALINGER M. A., Proc. Natl. Acad. Sci. U.S.A., 99 (2002) 2561.
21. BORLAND L., Phys. Rev. Lett., 89 (2002) 098701;
22. Quantit. Finance, 2 (2002) 415;
23. DUARTE QUEIRÓS S. M., to be published in Quantit. Finance (2005).
24. TSALLIS C., J. Stat. Phys., 52 (1988) 479. A regularly updated bibliography on the subject is avaible at http://tsallis.cat.cbpf.br/biblio.htm.
25. WILLMOTT P., Paul Willmott on Quantitative Finance (Wiley, Chichester) 2000;
26. AUSLOOS M. and IVANOVA K., Application of Econophysics: Proceedings of the Second Nikkei Econophysics Symposium, edited by TAKAYASU H. (Spinger-Verlag, Berlin) 2003.
27. GOPIKRISHNAN P., PLEROU V., GABAIX X. and STANLEY H. E., Phys. Rev. E, 62 (2000) R4493.
28. MARCHAND J.-P., Distributions (North-Holland, Amsterdam) 2003.
29. KOLB E., MAZOZI T., CLÉMENT E. and DURAN J., Eur. Phys. J. B, 8 (1999) 433;
30. BORGES E. P., Doctor Thesis, CBPF, Rio de Janeiro (2004).
31. Following v definition, ω should equal 1. Nonetheless, we will keep it in the presented form for reasons that will become clear later on.
32. FELLER W., Ann. Math., 54 (1951) 173.
33. HESTON S. L., Rev. Financ. Stud., 6 (1993) 327.
34. TAKAYASU H., SATO A.-H. and TAKAYASU M., Phys. Rev. Lett., 79 (1997) 966.
35. FRISCH U., Turbulence: The Legacy of A. Kolmogorov (Cambridge University Press, Cambridge) 1997;
36. BECK C., LEWIS G. S. and SWINNEY H. L., Phys. Rev. E, 63 (2001) R035303.
37. RISKEN H., The Fokker-Planck Equation: Methods of Solution and Applications (Springer-Verlag, Berlin) 1989.
38. GRADSHTEYN I. S. and RYZHIK I. R., Table of Integrals, Series and Products (Academic Press, New York) 1965.
39. DUARTE QUEIRÓS S. M., http://br.arxiv.org/abs/physics/0411111 working paper, 2004.
40. PERELLÓ J., MASOLIVER J. and BOUCHAUD J. P., Appl. Math. Fin., 11 (2004) 27.
41. LUX T. and MARCHESI M., Nature, 397 (1999) 498.
42. WILK G. and WŁODARCZYK Z., Phys. Rev. Lett., 84 (2000) 2770.
43. BECK C., Phys. Rev. Lett., 87 (2001) 180601;
44. Europhys. Lett., 57 (2002) 329.
45. BECK C. and COHEN E. G. D., Physica A, 322 (2003) 267.
46. SOUZA A. M. C. and TSALLIS C., Phys. Rev. E, 67 (2003) 026106.
47. This can be obtained from another stationary Feller process but for variable x = /ω.