英文标题：
《The Black-Scholes Equation in Presence of Arbitrage》
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作者：
Simone Farinelli and Hideyuki Takada
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最新提交年份：
2021
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英文摘要：
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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中文摘要：
我们应用几何套利理论来获得数学金融中的结果，这些结果在公式中不需要随机微分几何。首先，对于由多维It过程给出的一般市场动力学，我们指定并证明了（NFLVR）与预期效用最大化之间的等价性。作为副产品，我们提供了由零曲率（ZC）条件给出的（NUPBR）条件的几何特征。最后，我们将Black-Scholes偏微分方程扩展到允许套利的市常
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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