The Black-Scholes Equation in Presence of Arbitrage
32 Pages Posted: 20 Dec 2016 Last revised: 28 Jun 2019
Date Written: June 19, 2019
We apply Geometric Arbitrage Theory to obtain results in Mathematical Finance, which do not need stochastic differential geometry in their formulation.
First, for a generic market dynamics given by a multidimensional Itô's process we specify and prove the equivalence between (NFLVR) and expected utility maximization. As a by-product we provide a geometric characterization of the (NUPBR) condition given by the zero curvature (ZC) condition. Finally, we extend the Black-Scholes PDE to markets allowing arbitrage.
Keywords: Geometric Arbitrage, Black-Scholes PDE, Expected Utility Maximization
JEL Classification: C02
Suggested Citation: Suggested Citation