PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2011 | 9 | 3 | 865-873
Tytuł artykułu

Model of discrete dynamics of asset price relations based on the minimal arbitrage principle

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we present a deterministic and a probabilistic model of the dynamics of the price relations for a number of assets on the market. The formalism is based on the asset space introduced in a theory by Illinski. We derive, from an action functional for the system of price relations in that space, the corresponding difference equations, which constitute the deterministic description. Furthermore, we obtain the probability density function of the probabilistic model of market dynamics from the same action functional. The deterministic solution corresponds to a geometric sequence for the interest, whereas the derived probability density describes the probability of the next value of the price relations in dependence on their prior value. The formalism is completely developed for systems (markets) with two and three assets, but exactly the same approach is applicable to the systems consisting of an arbitrary number of assets.
Wydawca

Czasopismo
Rocznik
Tom
9
Numer
3
Strony
865-873
Opis fizyczny
Daty
wydano
2011-06-01
online
2011-02-26
Twórcy
  • Department of Electronic Systems and Information Processing, University of Zagreb, Faculty of Electrical Engineering and Computing, Unska 3, HR-10000, Zagreb, Croatia, zvonko.kostanjcar@fer.hr
autor
  • Department of Electronic Systems and Information Processing, University of Zagreb, Faculty of Electrical Engineering and Computing, Unska 3, HR-10000, Zagreb, Croatia, branko.jeren@fer.hr
Bibliografia
  • [1] K. Ilinski, Physics of Finance: Gauge Modeling in Non-equilibrium Pricing (Wiley, Chichester, 2001)
  • [2] J.P. Bouchaud, M. Potters, Theory of Financial Risks: From Statistical Physics to Risk Management (Cambridge University Press, Cambridge, 2000)
  • [3] M. Constantin, S. Das Sarma, Phys. Rev. E 72, 051106 (2005) http://dx.doi.org/10.1103/PhysRevE.72.051106[Crossref]
  • [4] B.G. Malkiel, A Random Walk Down Wall Street (W.W. Norton and Company, New York, 2003)
  • [5] B.E. Baaquie, Quantum Finance (Cambridge University Press, Cambridge, 2004) http://dx.doi.org/10.1017/CBO9780511617577[Crossref]
  • [6] N.F. Johnson, P. Jeffreies, P.M. Hui, Financial Market Complexity (Oxford University Press, Oxford, 2003) http://dx.doi.org/10.1093/acprof:oso/9780198526650.001.0001[Crossref]
  • [7] R. Cont, J.-P. Bouchaud, Macroecon. Dyn. 4, 170 (2000) http://dx.doi.org/10.1017/S1365100500015029[Crossref]
  • [8] A.W. Lo, C. Mackinlay, Rev. Financ. Stud. 1, 41 (1998) http://dx.doi.org/10.1093/rfs/1.1.41[Crossref]
  • [9] S. Drozdz, M. Forczek, J. Kwapien, P. Oswiecimka, R. Rak, Physica A 383, 59 (2007) http://dx.doi.org/10.1016/j.physa.2007.04.130[Crossref]
  • [10] A. Dionisio, R. Menezes, D.A. Mendes, Physica A 382, 58 (2007) http://dx.doi.org/10.1016/j.physa.2007.02.008[Crossref]
  • [11] A. Matacz, International Journal of Theoretical and Applied Finance 3, 143 (2000) http://dx.doi.org/10.1142/S0219024900000073[Crossref]
  • [12] X. Gabaix, P. Gopikrishnan, V. Plerou, H.E. Stanley, Nature 423, 267 (2003) http://dx.doi.org/10.1038/nature01624[Crossref]
  • [13] M. Fredrick, M.D. Johnson, Physica A 320, 525 (2003) http://dx.doi.org/10.1016/S0378-4371(02)01558-3[Crossref]
  • [14] J.P. Bouchaoud, Physica A 313, 238 (2002) http://dx.doi.org/10.1016/S0378-4371(02)01039-7[Crossref]
  • [15] R.N. Mantegna et al., Physica A 274, 216 (1999) http://dx.doi.org/10.1016/S0378-4371(99)00395-7[Crossref]
  • [16] J.D. Farmer, N. Zamani, Eur. Phys. J. B 55, 189 (2007) http://dx.doi.org/10.1140/epjb/e2006-00384-5[Crossref]
  • [17] G. Bonanno, F. Lillo, R.N. Mantegna, Physica A 299, 16 (2001) http://dx.doi.org/10.1016/S0378-4371(01)00279-5[Crossref]
  • [18] J.V. Andersen, S. Gluzman, D. Sornette, Eur. Phys. J. B 14, 579 (2000) http://dx.doi.org/10.1007/s100510051067[Crossref]
  • [19] Y. Bar-Yam, Dynamics of complex systems (Westview Press, Boulder, 1997)
  • [20] H. Haken, Information and Self-Organization (Springer, Berlin, 1999)
  • [21] N. Bocara, Modeling Complex systems (Springer, New York, 2004)
  • [22] G. Mack, arXiv:hep-th/0011074
  • [23] A. Shleifer, W.R. Vishny, J. Financ. 52, 35 (1997) http://dx.doi.org/10.2307/2329555[Crossref]
  • [24] K. Ilinski, J. Phys. A: Math. Gen. 33, L5 (2000) http://dx.doi.org/10.1088/0305-4470/33/1/102[Crossref]
  • [25] K. Ilinski, arXiv:cond-mat/9811197v1
  • [26] D. Sornette, Int. J. Mod. Phys. C 9, 505 (1998) http://dx.doi.org/10.1142/S0129183198000406[Crossref]
  • [27] J.C. Baez, J.W. Gilliam, Lett. Math. Phys. 31, 205 (1994) http://dx.doi.org/10.1007/BF00761712[Crossref]
  • [28] J.B. Chen, H.Y. Guo, K. Wu, Appl. Math. Comput. 177, 226 (2006) http://dx.doi.org/10.1016/j.amc.2005.11.002[Crossref]
  • [29] A.G. Lisi, arXiv:physics/0605068v1
  • [30] J.L. McCauley, Physica A 329, 199 (2003) http://dx.doi.org/10.1016/S0378-4371(03)00591-0[Crossref]
  • [31] D. Ruelle, Thermodynamic Formalism, The Mathematical Structures of Equilibrium Statistical Mechanics (Cambridge University Press, Cambridge, 2004) http://dx.doi.org/10.1017/CBO9780511617546[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-010-0093-x
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.