Abstract
The article presents a description of geometry of Banach structures forming mathematical base of markets arbitrage absence type phenomena. In this connection the role of reflexive subspaces (replacing classically considered finite-dimensional subspaces) and plasterable cones is uncovered.
Highlights
The article presents analysis of geometry of Banach structures that can be interpreted as certain arbitrage free markets type phenomena
The Fundamental Theorem of asset Pricing links arbitrage free markets (i.e markets that do not admit riskless claims yielding profit with strictly positive probability; the accurate definition will be given below in Section 1) with existence of martingales generated by measures that are equivalent to the initial one
We show that the principal Banach space objects that possess ’arbitarge free’ and ’martingale’ geometric behavior are plasterable cones and reflexive subspaces
Summary
A.V. Lebedev∗ Institute of Mathematics, University of Bialystok, ul. Akademicka 2, PL-15-267 Bialystok, Poland Department of Mechanics and Mathematics, Belarus State University, pr.
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