Banach geometry of financial market models
- Authors: Zabreiko P.P.1,2, Lebedev A.V.1,2
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Affiliations:
- Mechanics and Mathematics Faculty
- University of Bialystok
- Issue: Vol 95, No 2 (2017)
- Pages: 164-167
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/224947
- DOI: https://doi.org/10.1134/S106456241702020X
- ID: 224947
Cite item
Abstract
Banach geometric objects imitating a phenomenon of the type of the absence of arbitrage in financial markets models are analyzed. The role played in this field by reflexive subspaces (which replace classically considered finite-dimensional subspaces) and by plasterable cones is revealed. A series of new geometric criteria for the absence of arbitrage are proved. An alternative description of the existence of a martingale measure is given, which does not use dual objects.
About the authors
P. P. Zabreiko
Mechanics and Mathematics Faculty; University of Bialystok
Email: lebedev@bsu.by
Belarus, Minsk, 220050; Bialystok
A. V. Lebedev
Mechanics and Mathematics Faculty; University of Bialystok
Author for correspondence.
Email: lebedev@bsu.by
Belarus, Minsk, 220050; Bialystok