论文标题
部分可观测时空混沌系统的无模型预测
The Russian Option with A Random Time Horizon
论文作者
论文摘要
本文旨在为俄罗斯选项提供独特的评估公式，并随机时间范围。特别是，此类选项限制了其持有人，以在基础资产的最高运行最大值的最后一次退出时间之前制定停止规则。通过与随机时间相关的过滤的扩大理论，可以将这个定价问题转化为同等的最佳停止问题，其中半连续，依赖时间的增益函数在某些点的部分导数是单数的。尽管增益函数的这些不愉快的特征，但我们选择了参数，我们确定了自由边界的单调性和价值函数的规律性，这反过来又导致我们解决了所需的自由边界问题。之后，得出了表征自由边界和值函数的非线性积分方程。我们还详细介绍了这些方程的解决方案。
This paper is intended to provide a unique valuation formula for the Russian option with a random time horizon; in particular, such option restricts its holders to make their stopping rules before the last exit time of the price of the underlying asset at its running maximum. By the theory of enlargement of filtrations associated with random times, this pricing problem can be transformed into an equivalent optimal stopping problem with a semi-continuous, time-dependent gain function whose partial derivative is singular at certain point. Despite these unpleasant features of the gain function, with our choice of the parameters, we establish the monotonicity of the free boundary and the regularity of the value function, which in turn lead us to the desired free-boundary problem. After this, the nonlinear integral equations that characterise the free boundary and the value function are derived. We also examine the solutions to these equations in details.
