IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Geometry of Financial Markets - Towards Information Theory Model of Markets

Listed author(s):
  • Edward W. Piotrowski


  • Jan Sladkowski


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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: no

Paper provided by University of Bialtystok, Department of Theoretical Physics in its series Departmental Working Papers with number 26.

in new window

Date of creation:
Handle: RePEc:sla:eakjkl:26
Contact details of provider: Postal:
Institute of Physics, Uniwersytecka 4, Pl-40007 Katowice

Phone: (+48)322588431
Fax: (+48)322588431
Web page:

More information through EDIRC

No references listed on IDEAS
You can help add them by filling out this form.

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

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: ()

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.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with 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 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.