Black-Scholes边值问题通解的推导
Derivation of the General Solution of the Black-Scholes Boundary-Value Problem
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中文总结 AI 辅助
本文严格推导了满足Black-Scholes方程及欧式看涨期权终端条件的无穷多个解，证明原公式非唯一解，违反一价定律。
中文摘要 AI 辅助
存在无穷多个函数满足Black-Scholes偏微分方程及对应于欧式看涨期权的终端条件。这意味着曾获1997年诺贝尔经济学奖的Black-Scholes公式并非如曾经所假设的那样是唯一解。因此，它违反了经济学和金融学基本定律之一的一价定律。在本文中，我们给出了这些Black-Scholes边值问题解的严格推导。
英文摘要
There are infinitely many functions that satisfy the Black-Scholes partial differential equation and the terminal condition corresponding to the European call option. This means that the Black-Scholes formula, which led to the award of the 1997 Nobel Prize in Economic Sciences, is not the unique solution, as was once assumed. Consequently, it violates the law of one price, one of the fundamental laws of economics and finance. In this article, we present a rigorous derivation of these solutions to the Black-Scholes boundary value problem.
