2019/04/17 by Farinelli, Simone, Takada, Hideyuki
#60D05 #91G10 #91G20 #91G80 #FOS: Economics and business #Pricing of Securities (q-fin.PR) #Risk Management (q-fin.RM)
paper · doi:10.48550/arxiv.1904.11565
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.