IDEAS home Printed from https://ideas.repec.org/p/sla/eakjkl/26.html
   My bibliography  Save this paper

Geometry of Financial Markets - Towards Information Theory Model of Markets

Author

Listed:
  • Edward W. Piotrowski

    ()

  • Jan Sladkowski

    ()

Abstract

Most of parameters used to describe states and dynamics of financial market depend on proportions of the appropriate variables rather than on their actual values. Therefore, projective geometry seems to be the correct language to describe the theater of financial activities. We suppose that the object of interest of agents, called here baskets, form a vector space over the reals. A portfolio is defined as an equivalence class of baskets containing assets in the same proportions. Therefore portfolios form a projective space. Cross ratios, being invariants of projective maps, form key structures in the proposed model. Quotation with respect to an asset X (i.e. in units of X) are given by linear maps. Among various types of metrics that have financial interpretation, the min-max metrics on the space of quotations can be introduced. This metrics has an interesting interpretation in terms of rates of return. It can be generalized so that to incorporate a new numerical parameter (called temperature) that describes agent's lack of knowledge about the state of the market. In a dual way, a metrics on the space of market quotation is defined. In addition, one can define an interesting metric structure on the space of portfolios/quotation that is invariant with respect to hyperbolic (Lorentz) symmetries of the space of portfolios. The introduced formalism opens new interesting and possibly fruitful fields of research.

Suggested Citation

  • Edward W. Piotrowski & Jan Sladkowski, "undated". "Geometry of Financial Markets - Towards Information Theory Model of Markets," Departmental Working Papers 26, University of Bialtystok, Department of Theoretical Physics.
  • Handle: RePEc:sla:eakjkl:26
    as

    Download full text from publisher

    File URL: http://alpha.uwb.edu.pl/ep/RePEc/sla/eakjkl/26.pdf
    Download Restriction: no

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. F. Bagarello & E. Haven, 2014. "Towards a formalization of a two traders market with information exchange," Papers 1412.8725, arXiv.org.
    2. Szczypińska, Anna & Piotrowski, Edward W., 2008. "Projective market model approach to AHP decision making," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3982-3986.
    3. Szczypińska, Anna & Piotrowski, Edward W., 2009. "Inconsistency of the judgment matrix in the AHP method and the decision maker’s knowledge," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 907-915.
    4. E. W. Piotrowski & M. Schroeder, 2007. "Kelly criterion revisited: optimal bets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(2), pages 201-203, May.
    5. Anna Szczypinska & Edward W. Piotrowski, "undated". "Projective Market Model Approach to AHP Decision-Making," Departmental Working Papers 32, University of Bialtystok, Department of Theoretical Physics.
    6. Edward W. Piotrowski & Jerzy Luczka, "undated". "The relativistic velocity addition law optimizes a forecast gambler's profit," Departmental Working Papers 31, University of Bialtystok, Department of Theoretical Physics.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sla:eakjkl:26. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: http://edirc.repec.org/data/epslapl.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.