  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.
