The Black-Scholes Equation in Presence of Arbitrage

Simone Farinelli and Hideyuki Takada

Papers from arXiv.org

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.

Date: 2019-04, Revised 2021-10
New Economics Papers: this item is included in nep-upt
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1904.11565

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