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arXiv · 1904.11565

The Black-Scholes Equation in Presence of Arbitrage

Simone Farinelli·Hideyuki Takada
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Abstract

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 It\^o'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.

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Simone Farinelli, Hideyuki Takada. 2019-04-17. The Black-Scholes Equation in Presence of Arbitrage. https://arxiv.org/abs/1904.11565

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