美式選擇權的數值模擬方法已有大量的文獻與相關研究可供參考，然後其背後的理論與背景的推導過程文獻較為缺乏，因此本文將以Black-scholes模型為基礎，再利用漂移布朗運動之第一次執行時間的Laplace 轉換與 Stopping Time的性質來推導最佳Stopping Time選擇權在無發放股利與發放股利的評價模型。 There are many articles and papers of numerical method for pricing American option to study，but it has less background of theorem than pricing American option. Therefore，this articles will use the property of Laplace transform for the first passing time of drifted Brownian Motion and Stopping Time basic on Black-Scholes Model to compute the Models of Optimal Stopping Time Option with no dividend and dividend.
