Geometry of financial markets-Towards information theory model of markets

Physica A: Statistical Mechanics and its Applications

Volumn 382, Issue 1, 2007, Pages 228-234

  Piotrowski, Edward W ^a   Sładkowski, Jan ^b  

^a UNIVERSITY OF BIALYSTOK   (Poland)

^b UNIVERSITY OF SILESIA   (Poland)

Author keywords

Econophysics; Finance; Portfolio theory; Projective geometry

Indexed keywords

INFORMATION THEORY; INVENTORY CONTROL;

ECONOPHYSICS; FINANCIAL INTERPRETATION; PORTFOLIO THEORY; PROJECTIVE GEOMETRY;

FINANCE;

EID: 34249811482     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2007.02.020     Document Type: Article

References (22)

1. An invariant of a process (phenomenon, transformation, etc.) is a numerical parameter whose value remains constant during that process. Analogously, a covariant is a parameter whose numerical value has only in a (relative) sense a preselected coordinate system but changes in a specified way if the coordinate system is changed (e.g. given by some symmetry transformation).
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3. Most of the axioms take the same form as in standard models because they simply define market organization.
4. We could also take the empty basket into consideration but this would spoil the projective space interpretation.
5. Note that this means that we treat all taxes, brokerages, etc. as liabilities and therefore as separate assets. In this way we are not forced to consider friction in the model. Models that have scale effects (projective symmetry is broken) should have a dual description in terms of non-transitive quotations.
6. A balanced portfolio is an analogue of a photon, cf. the discussion hyperbolic geometry.
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9. Due to physical constraints there is a maximum propagation speed (speed of light). In our model, the portfolio "propagation" is limited when the portfolio became balanced-you have no money for further purchases.
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