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Geometric arbitrage theory reformulates a generic asset model possiblyallowing for arbitrage by packaging all asset and their forward dynamics into astochastic principal fibre bundle, with a connection whose parallel transportencodes discounting and portfolio rebalancing, and whose curvature measures, inthis geometric language, the instantaneous arbitrage capability generated bythe market itself. The asset and market portfolio dynamics have a quantummechanical description, which is constructed by quantizing the deterministicversion of the stochastic Lagrangian system describing a market allowing forarbitrage. Results, obtained by solving the Schroedinger equation, coincidewith those obtained by solving the stochastic Euler Lagrange equations derivedby a variational principle and providing therefore consistency.

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