title: The Geometric Phase of Stock Trading.
abstract: Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote.
authors.affiliation: Division of Automatic Control, Dept. of Electrical Engineering, Linköping University, SE-58183, Linköping, Sweden.
authors.forename: Claudio
authors.identifier: http://orcid.org/0000-0003-4142-6502
authors.initials: C
authors.lastname: Altafini
mesh_terms: D000465:Algorithms; D007449:Investments; D008962:Models, Theoretical