雙邊最佳停止問題和永續美式勒式選擇權

Abstract

本論文在研究永續美式勒式選擇權在超指數型跳躍擴散模型下的定價問題。利用自由邊界問題的方法，我們解決了所對應之最佳停止時間問題，並且求出永續美式勒式選擇權的合理價格。此外，我們也證明了自由邊界問題再加上平滑銜接條件的解之存在性。

This study investigates the problem of pricing perpetual American strangle option under a hyper-exponential jump-diffusion model. By using the free boundary problem approach, we solve the corresponding optimal stopping problem and determine the rational price of the perpetual American strangle options. In particular, we prove the existence of solutions to the free boundary problems with the smooth pasting conditions.