The Black-Scholes Equation in Presence of Arbitrage
| Autor: | Simone Farinelli, Hideyuki Takada |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Mathematical finance
Zero (complex analysis) Black–Scholes model Characterization (mathematics) Curvature FOS: Economics and business Differential geometry Computer Science::Computational Engineering Finance and Science Risk Management (q-fin.RM) Applied mathematics Pricing of Securities (q-fin.PR) Arbitrage Quantitative Finance - Pricing of Securities Equivalence (measure theory) Quantitative Finance - Risk Management 91G10 91G20 91G80 60D05 Mathematics |
| Zdroj: | SSRN Electronic Journal. |
| ISSN: | 1556-5068 |
| DOI: | 10.2139/ssrn.2887425 |
| Popis: | 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. Comment: The assumptions of Proposition 23 were corrected after Claudio Fontana provided us with a counterexample for the previous version of this proposition. arXiv admin note: substantial text overlap with arXiv:1509.03264, arXiv:1906.07164, arXiv:1406.6805, arXiv:0910.1671 |
| Databáze: | OpenAIRE |
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