Continuous-time random-walk model for financial distributions

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 67, Issue 2 1, 2003, Pages 211121-2111210

  Masoliver, Jaume ^a   Montero, Miquel ^a   Weiss, George H ^b  

^a UNIVERSITY OF BARCELONA   (Spain)

^b NATIONAL INSTITUTES OF HEALTH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FINANCIAL DATA PROCESSING; PRIMARY BATTERIES; PROBABILITY; PROBLEM SOLVING;

RANDOM WALK MODEL;

RANDOM PROCESSES;

EID: 0038057471     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (31)

1. E.W. Montroll and G.H. Weiss, J. Math. Phys. 6, 167 (1965).
2. E.W. Montroll and M.F. Shlesinger, in Nonequilibrium Phenomena II: From Stochastics to Hydrodynamics, edited by J. L. Lebowitz and E.W. Montroll (North-Holland, Amsterdam, 1984).
3. G.H. Weiss, Aspects and Applications of the Random Walk (North-Holland, Amsterdam, 1994).
4. H. Scher and E.W. Montroll, Phys. Rev. B 12, 2455 (1975).
5. G.H. Weiss, J.M. Porrà, and J. Masoliver, Phys. Rev. E 58, 6431 (1998); Opt. Commun. 146, 268 (1998).
6. G.H. Weiss, J.M. Porrà, and J. Masoliver, Phys. Rev. E 58, 6431 (1998); Opt. Commun. 146, 268 (1998).
7. A.H. Gandjbakhche and G.H. Weiss, Phys. Rev. E 61, 6958 (2000).
8. B. Berkowitz and H. Scher, Phys. Rev. Lett. 79, 4038 (1997).
9. M. Boguna and A. Corral, Phys. Rev. Lett. 78, 4950 (1997).
10. A.M. Berezhkovskii and G. Sutmann, Phys. Rev. E 65, 060201 (2002).
11. E. Gudowska-Nowak and K. Weron, Phys. Rev. E 65, 011103 (2002).
12. R. Balescu, Phys. Rev. E 55, 2465 (1997).
13. R. Kutner, Chem. Phys. 284, 481 (2002); Comput. Phys. Commun. 147, 565 (2002).
14. R. Kutner, Chem. Phys. 284, 481 (2002); Comput. Phys. Commun. 147, 565 (2002).
15. A. Helmstetter and D. Sornette, Phys. Rev. E (to be published), e-print http://arXiv.org/abs/cond-mat/0203505.
16. The Random Character of Stock Market Prices, edited by P.H. Cootner (MIT Press, Cambridge, MA, 1964).
17. M.F.M. Osborne, Oper. Res. 7, 145 (1959).
18. 0 = 0 without loss of generality.
19. M.G. Kendall, J. R. Stat. Soc. Ser. A. Gen. 96, 11 (1953).
20. B. Mandelbrot, J. Business 35, 394 (1963).
21. R.N. Mantegna and E.H. Stanley, Nature (London) 376, 46 (1995).
22. J. Masoliver, M. Montera, and J.M. Porrà, Physica A 283, 559 (2000).
23. This is precisely the approach taken by Kutner [12] although his approximation is circumscribed within the frame of Weierstrass walks in which an specific form of the function ρ(x,t) is obtained under the assumptions of Poissonian waiting times and self-similarity. As we will see next our formalism includes this approach.
24. This condition guarantees that ρ̃(ω,t) defined by Eq. (9) is a characteristic function. See E. Lukacs, Characteristic Functions (Griffin, London, 1970).
25. W. Magnus, F. Oberhettinger, and R.P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics (Springer-Verlag, New York, 1966).
26. Tic-by-tic data have been provided by the Futures Industries Institute (Washington, DC). The dollar-mark future exchange has been the object of numerous works (see, for instance, Ref. [25]).
27. C.J.G. Evertsz, Fractals 3, 609 (1995).
28. V. Plerou, P. Gopikrishnan, L.A. Nunes Amaral, M. Meyer, and H.E. Stanley, Phys. Rev. E 60, 6519 (1999).
29. P. Gopikrishnan, V. Plerou, L.A. Nunes Amaral, M. Meyer, and H.E. Stanley, Phys. Rev. E 60, 5305 (1999).
30. F. Mainardi, M. Roberto, R. Gorenflo, and E. Scalas, Physica A 287, 468 (2000).
31. M.J. Lighthill, An Introduction to Fourier Analysis and Generalized Functions (Cambridge University Press, Cambridge, 1980).