Modern rheology on a stock market: Fractional dynamics of indices

Acta Physica Polonica A

Volumn 118, Issue 4, 2010, Pages 677-687

  Kozlowska M ^a   Kutner, R ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

BIOPOLYMERS; CALCULATIONS; COMMERCE; DYNAMICS; ELASTICITY; EXPONENTIAL FUNCTIONS; FINANCIAL MARKETS; FUNCTIONS; INTEGRAL EQUATIONS;

APPROXIMATE SOLUTION; DETERMINISTIC MODELING; FRACTIONAL INTEGRAL EQUATIONS; GENERALIZED EXPONENTIAL FUNCTIONS; MITTAG-LEFFLER FUNCTIONS; NON-DEBYE RELAXATION; RHEOLOGICAL MODELING; UNCERTAINTY PRINCIPLES;

FINANCE;

EID: 77958132375     PISSN: 05874246     EISSN: 1898794X     Source Type: Journal    
DOI: 10.12693/APhysPolA.118.677     Document Type: Article

References (43)

1. M. Kozłowska, A. Kasprzak, R. Kutner, Int. J. Mod. Phys. C 19, 453 (2008).
2. D. Sornette, Why Stock Markets Crash. Critical Events in Complex Financial Systems, Princeton University Press, Princeton 2003.
3. C. Tsallis, Braz. J. Phys. 39, 337 (2009).
4. B.M. Roehner, Patterns of Speculation. A Study in Observational Econophysics, Cambridge University Press, Cambridge UK 2002.
5. M. Ausloos, in: Econophysics and Sociophysics. Trends and Perspectives, Eds. B.K. Chakrabarti, A. Chakraborti, A. Chatterjee, Wiley-VCH Verlag, Weinheim 2006, Ch. 9, p. 249.
6. W.-X. Zhou, D. Sornette, Physica A 330, 543 (2003).
7. W.-X. Zhou, D. Sornette, Physica A 330, 584 (2003).
8. P. Gnaciński, D. Makowiec, Physica A 344, 322 (2004).
9. S. Drożdż, F. Grummer, F. Ruf, J. Speth, Physica A 324, 174 (2003).
10. S. Drożdż, J. Kwapień, P. Oświ̧ecimka, J. Speth, Acta Phys. Pol. A 114, 539 (2008).
11. D. Sornette, A. Johansen, J.-P. Bouchaud, J. Phys. I France 6, 167 (1996).
12. D. Sornette, A. Johansen, Physica A 245, 411 (1997).
13. D. Sornette, A. Johansen, Quant. Finance 1, 452 (2001).
14. A. Johansen, D. Sornette, J. Risk 4, 69 (2001).
15. A. Johansen, Comment on Are financial crashes predictble? by L. Laloux, M. Potters, R. Cont, J.-P. Aguilar, J.-P. Bouchaud, Europhysics Lett. 60 (5), 809 (2002).
16. D. Grech, Z. Mazur, Acta Phys. Pol. B 36, 2403 (2005).
17. R. Badii, A. Politi, Complexity. Hierarchical Structures and Scaling in Physics, Cambridge University Press, Cambridge UK 1997.
18. W. Paul, J. Baschnagel, Stochastic Processes. From Physics to Finance, Springer-Verlag, Berlin 1999.
19. R.N. Mantegna, H.E. Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance, Cambridge University Press, Cambridge UK 2000.
20. J.-P. Bouchaud, M. Potters, Theory of Financial Risks. From Statistical Physics to Risk Management, Cambridge University Press, Cambridge UK 2001.
21. K. Ilinski, Physics of Finance. Gauge Modelling in Non-Equilibrium Pricing, Wiley, Chichester 2001.
22. E. Scales, R. Gorenflo, F. Mainardi, Phys. Rev. E 69, 011107 (2004).
23. L. Sabatellil, S. Keating, J. Dudley, P. Richmond, Eur. Phys. J. B 27, 273 (2002).
24. Special Issue & Directory, Nonextensive Statistical Mechanics: New Trends, New Perspectives, Euro-physicsnews 36/6 (2005).
25. F. Schweitzer, Brownian Agents and Active Particles, Springer-Verlag, Berlin 2003.
26. A. Bunde, J. Kantelhardt, Phys. Blätter 57, 49 (2001).
27. R. Cont, J.-P. Bouchaud, Macroecon. Dyn. 4, 170 (2000).
28. H. Schiessel, Chr. Friedrich, Blumen, in Applications of Fractional Calculus in Physics, Ed. R. Hilfer, World Scientific, Singapore 2000, Chap. 7, pp. 331-376.
29. Th.F. Nonnenmacher, R. Metzler, Applications of Fractional Calculus in Physics, Ed. R. Hilfer, World Sci., Singapore 2000, Ch. 8, p. 377.
30. N. Tschoegel, The Phenomenological Theory of Linear Viscoelastic Behavior, Springer-Verlag, Berlin 1989.
31. R. Richert, A. Blumen, Disorder Effects on Relax-ational Processes: Glasses, Polymers, Proteins, Eds. R. Richert, A. Blumen, Springer, Berlin 1994, Ch. 1, p. 1.
32. R. Metzler, J. Klafter, Phys. Rep. 339, 1 (2000).
33. P.L. Butzer, U. Westphal, Applications of Fractional Calculus in Physics, Ed. R. Hilfer, World Sci., Singapore 2000, Ch. 1 p. 1.
34. F. Mainardi, M. Raberto, R. Gorenflo, E. Scales, Physica A 287, 468 (2000).
35. R. Kutner, F. Świtała, Qunatitative Finance 3, 201 (2003).
36. H. Schiessel, A. Blumen, J. Phys. A: Math. Gen. 26, 5057 (1995).
37. W.G. Glöckle, Th.F. Nonnenmacher, Macromolecules 24 6426 (1991).
38. W.G. Glöckle, Th.F. Nonnenmacher, Rheol. Acta 33, 337 (1994).
39. P. Richmond, S. Hutzler, R. Coelho, P. Reptowicz, in Ref. [9], Ch. 5, p. 131.
40. S. Iyazima, K. Yamamoto, in: Practical Fruits of Econophysics. Proceedings of the Third Nikkei Econophysics Symposium, Ed. H. Takayasu, Springer-Verlag, Berlin 2006, p. 344.
41. K. Yamamoto, S. Miyazima, H. Yamamoto, T. Oht-suki, A. Fujihara, in Ref. [40], p. 349.
42. M. Jagielski, R. Kutner, Acta Phys. Pol. A 118, 615 (2010).
43. E. Borgonovo, L. Peccati, in: Uncertainty and Risk, Eds. M. Abdellaoni, R.D. Luce, M.J. Machina, B. Munier, Springer-Verlag, Berlin 2007, Part I, p. 41.