We have embedded the classical theory of stochastic finance into a differential geometric framework called Geometric Arbitrage Theory and show that it is possible to:
--Write arbitrage as curvature of a principal fibre bundle.
--Parameterize arbitrage strategies by its holonomy.
--Give the Fundamental Theorem of Asset Pricing a differential homotopic characterization.
--Characterize Geometric Arbitrage Theory by five principles and show they they are consistent with the classical theory of stochastic finance.
--Derive for a closed market the equilibrium solution for market portfolio and dynamics in the cases where:
-->Arbitrage is allowed but minimized.
-->Arbitrage is not allowed.
--Prove that the no-free-lunch-with-vanishing-risk condition implies the zero curvature condition. The converse is in general not true and additionally requires the Novikov condition for the instantaneous Sharpe Ratio Dynamics to be satisfied.