Financial market equilibrium in notions of Finsler geometry, symplectic geometry and integral geometry

Nowadays, it is of significant importance in financial market to pay attention to dynamics and quality of the properties of variables. In this regards, baskets and portfolios as the agents’ interests can be translated in notions of vector spaces and their equivalence classes. In this way, these main concepts of projective spaces describe development of these marketing parameters. As mentioned in (Piotrowski and Stadkowski, 2007), the number of times that portfolio is balanced for quotation in marketing is equivalent to the number of points that lie on the quotation hyperplane in projective geometry . For geometric extension of this idea and by a change of viewpoint, this parameter has been calculated by surface area of convex body of the corresponding projective spaces and Holmes-Thompson volume in notions of Finsler geometry, symplectic geometry and integral geometry. It can give an accurate tool for presenting the exact solution of economic problems. As a corollary of this methodology, it has been shown that the highest number of risks in market equilibrium can be obtained by the minimality of the volume in corresponding notions of these geometries.

Keywords:

Financial market , Risk , Finsler geometry , Symplectic geometry , Fourier transform