摘要翻译：
在等价局部鞅测度下，当股票价格为严格局部鞅过程时，与欧式期权相关的Black-Scholes偏微分方程可能存在多个解。本文研究了这类欧式期权的最小套期保值价格的逼近。我们的结果表明，一类回扣障碍期权可以用于这种近似。其中，一个特定的回扣选项还提供了一个连续回扣函数，它对应于相关抛物型偏微分方程的唯一经典解。这样的结构使得现有的数值偏微分方程技术可用于其计算。在适当的条件下，研究了敲除势垒向无穷远移动时的一个渐近收敛速度。
---
英文标题：
《Approximating Functional of Local Martingale Under the Lack of
  Uniqueness of Black-Scholes PDE》
---
作者：
Qingshuo Song
---
最新提交年份：
2012
---
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
--
一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
--
一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
--

---
英文摘要：
  When the underlying stock price is a strict local martingale process under an equivalent local martingale measure, Black-Scholes PDE associated with an European option may have multiple solutions. In this paper, we study an approximation for the smallest hedging price of such an European option. Our results show that a class of rebate barrier options can be used for this approximation. Among of them, a specific rebate option is also provided with a continuous rebate function, which corresponds to the unique classical solution of the associated parabolic PDE. Such a construction makes existing numerical PDE techniques applicable for its computation. An asymptotic convergence rate is also studied when the knocked-out barrier moves to infinity under suitable conditions.
---
PDF链接：
https://arxiv.org/pdf/1102.2285