When Risks and Uncertainties Collide: Mathematical Finance for Arbitrage Markets in a Quantum Mechanical View

Simone Farinelli and Hideyuki Takada

Papers from arXiv.org

Abstract: Geometric arbitrage theory reformulates a generic asset model possibly allowing for arbitrage by packaging all asset and their forward dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and portfolio rebalancing, and whose curvature measures, in this geometric language, the instantaneous arbitrage capability generated by the market itself. The asset and market portfolio dynamics have a quantum mechanical description, which is constructed by quantizing the deterministic version of the stochastic Lagrangian system describing a market allowing for arbitrage. Results, obtained by solving the Schroedinger equation, coincide with those obtained by solving the stochastic Euler Lagrange equations derived by a variational principle and providing therefore consistency.

Date: 2019-06, Revised 2021-01
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/1906.07164 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1906.07164

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().