标题： 内幕模型中带有逐步扩展滤过的永久美式标准和回顾期权 显示英文标题

标题： Perpetual American Standard and Lookback Options in Insider Models with Progressively Enlarged Filtrations

摘要： 我们推导了与在扩展的Black-Merton-Scholes模型中永续美式标准和回顾看跌和看涨期权定价相关的最优停止问题的显式解，该模型的filtrations逐步扩大。 更具体地说，内部人士可用的信息通过布朗filtrations建模，这些filtrations在无限时间区间内以基础风险资产价格的全局最大值或最小值的时间逐步扩大，而这些时间在由基础风险资产生成的filtrations中并不是停止时间。 我们证明了最优执行时间是资产价格过程首次达到下限或上限的时间，这取决于在发生全局最大值或最小值时间的情况下其运行最大值或最小值的当前值。 证明基于将原始问题转化为必要三维度最优停止问题和等价自由边界问题。 我们应用正常反射或正常进入条件以及价值函数的平滑贴合条件，以将候选边界表征为相关一阶非线性常微分方程和超越算术方程的最大或最小解。 显示英文摘要

摘要： We derive closed-form solutions to the optimal stopping problems related to the pricing of perpetual American standard and lookback put and call options in the extensions of the Black-Merton-Scholes model with progressively enlarged filtrations. More specifically, the information available to the insider is modelled by Brownian filtrations progressively enlarged with the times of either the global maximum or minimum of the underlying risky asset price over the infinite time interval, which is not a stopping time in the filtration generated by the underlying risky asset. We show that the optimal exercise times are the first times at which the asset price process reaches either lower or upper stochastic boundaries depending on the current values of its running maximum or minimum given the occurrence of times of either the global maximum or minimum, respectively. The proof is based on the reduction of the original problems into the necessarily three-dimensional optimal stopping problems and the equivalent free-boundary problems. We apply either the normal-reflection or the normal-entrance conditions as well as the smooth-fit conditions for the value functions to characterise the candidate boundaries as either the maximal or minimal solutions to the associated first-order nonlinear ordinary differential equations and the transcendental arithmetic equations, respectively.