Banach Geometry of Financial Market Models

P. P. Zabreikoa,b and A. V. Lebedeva,b,*
Translated by O. Sipacheva

a Mechanics and Mathematics Faculty, Belarussian State University, Minsk, 220050 Belarus

b University of Bialystok, Bialystok, Poland

Correspondence to: *e-mail:

Received 9 December, 2016

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.

DOI: 10.1134/S106456241702020X