When Risks and Uncertainties Collide: Quantum Mechanical Formulation of Mathematical Finance for Arbitrage Markets
51 Pages Posted: 20 Jun 2019 Last revised: 8 Jul 2019
Date Written: June 28, 2019
Geometric Arbitrage Theory reformulates a generic asset model possibly allowing for arbitrage by packaging all assets and their forwards 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 explicitly the Schrödinger equations by means of spectral decomposition of the Hamilton operator, coincides with those obtained by solving the stochastic Euler Lagrange equations derived by a variational principle and providing therefore consistency. Arbitrage bubbles are computed.
Keywords: Geometric Arbitrage, Arbitrage Bubbles, Minimal Arbitrage Dynamics
JEL Classification: C02, D58, D90, G11, G12
Suggested Citation: Suggested Citation