Geometric Arbitrage Theory and Market Dynamics Reloaded

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.