College of Engineering, University of Tehran (Guilan, Iran)
The developing of the financial market contributes to paying attention to analyses its dynamics and quality of properties of the variables. The results of the analysis showed that among the complex technical applications the geometry approach in this area is an advanced method to explain the financial market behaviour. This paper expands the idea that the portfolio is balanced for quotation in marketing is equivalent to the number of points that lie on the quotation hyperplane in projective geometry has been extended in geometric concepts. In this paper, the new geometric approach was proposed to estimate the number of times the portfolio is balanced for quotation. In fact, the calculations were made in terms of the volume of the Halmos-Thomson (as the bridge between Feinsler geometry, integral geometry, and symplectic geometry). The highest number of risks in market equilibrium was mentioned in the geometric concepts mentioned. In this way, the proposed geometric approach allows to analyse situations with a portfolio under different conditions: financial market equilibrium, reduce the risk of investment risk, and others developments in the stock market. The author calculates the parameters through the surface area of a convex body of the corresponding projective spaces and Holmes-Thompson volume in notions of integral geometry (Radon and Fourier transform), Finsler Geometry (and Minkowski spaces) and symplectic geometry. Contrary to existing numerical methods, this approach allows one to reach the analytic solution and also, concludes that the highest number of risks in market equilibrium can be obtained by minimality of the introduced volume.
Keywords: financial market, risk, Minkowski space, Finsler metric, Fourier transform.
JEL Classification: B16, D81, G32.
Cite as: Hasan-Zaden, A. (2018). Geometric modelling of portfolio and risk in market equilibrium. Marketing and Management of Innovations, 2, 210-217. https://doi.org/10.21272/mmi.2018.2-17
This work is licensed under a Creative Commons Attribution 4.0 International License
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