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. - Extend the Fundamental
Theorem of Asset Pricing by a differential homotopic characterization for both
complete and not complete arbitrage free markets.

- Characterize geometric arbitrage theory by five principles and show they
they are compatible 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 is equivalent to
the existence of a utility maximizer.