Banach geometry of arbitrage free markets
A. V. Lebedev, P. P. Zabreiko
TL;DR
This paper explores the geometric structure of arbitrage-free markets using Banach space theory, emphasizing the roles of reflexive subspaces and plasterable cones in understanding market phenomena.
Contribution
It introduces a Banach geometric framework for arbitrage-free markets, highlighting the importance of reflexive subspaces and plasterable cones in this context.
Findings
Reflexive subspaces are key in the geometric description of arbitrage-free markets.
Plasterable cones play a significant role in the Banach space model of market phenomena.
The geometric approach provides new insights into market arbitrage conditions.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.