存在套利情形下的 Black-Scholes 方程
证券定价
2021-10-13 v5 风险管理
摘要
我们应用几何套利理论获得数学金融中的结果，这些结果在表述上不需要随机微分几何。首先，对于由多维 It\^o 过程给出的通用市场动态，我们明确并证明了（NFLVR）与期望效用最大化之间的等价性。作为副产品，我们给出了由零曲率（ZC）条件给出的（NUPBR）条件的几何刻画。最后，我们将 Black-Scholes PDE 推广到允许套利的市场。
引用
@article{arxiv.1904.11565,
title = {The Black-Scholes Equation in Presence of Arbitrage},
author = {Simone Farinelli and Hideyuki Takada},
journal= {arXiv preprint arXiv:1904.11565},
year = {2021}
}
备注
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