Abstract
We review some recent results concerning some toy models of stock markets. Our models are suggested by the discrete nature of the number of shares and of the cash which are exchanged in a real market, and by the existence of conserved quantities, like the total number of shares or some linear combination of the cash and the shares. This suggests to use the same tools used in quantum mechanics and, in particular, the Heisenberg picture to describe the time behavior of the portfolio of each trader. We finally propose the use of this same framework in other sociological contexts.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bagarello F. (2006) An operatorial approach to stock markets. J. Phys. A 39: 6823–6840
Bagarello F., Morchio G. (1992) Dynamics of mean field spin models from basic results in abstract differential equations. J. Stat. Phys. 66: 849–866
Buffet E., Martin P.A. (1978) Dynamics of the open BCS model. J. Stat. Phys. 18(6): 585–632
Challet D., Marsili M. (2000) Phase transition and symmetry breaking in the minority game. Phys. Rev. E 60: 6271
Schaden M. (2002) A quantum approach to stock price fluctuations. Physica A 316: 511
Thirring, W., Wehrl, A.: On the mathematical structure of the B.C.S.-model. Commun. Math. Phys. 4, 303–314 (1967)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bagarello, F. The Heisenberg picture in the analysis of stock markets and in other sociological contexts. Qual Quant 41, 533–544 (2007). https://doi.org/10.1007/s11135-007-9076-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11135-007-9076-4