不确定环境下的进入：退出决策

　　Entry-exit decisions apply to numerous practical problems. For example， when to extract oil and when to stop the extraction， when to issue a new policy and when to end it， and when to let a kind of product enter a market and when to let the product exit the market， etc. Therefore， entry-exit decision problems attract a lot of researchers.There are three approaches to study entry-exit decisions， namely， real option， pure probability and optimal stopping. In this monograph， we appeal to optimal stopping to deal with entry-exit decisions. The main reasons are as follows. On the one hand， in the real option framework， the regularity of payoff functions is a priori assumed， while the optimal stopping approach intends to prove it. On the other hand， although the pure probability and optimal stopping approaches are both to solve a optimal stopping problem， we have to calculate density functions of some stopping times if applying the pure probability approach， which is not easy， whereas the optimal stopping one avoids such calculations.We aim to obtain closed-form solutions of optimal entry-exit decisions for the cases： costs depending on underlying processes， implementation with delay， and underlying processes following geometric Levy processes. In addition， we provide a complete theory for optimal stopping problems with regime switching， and use it to solve an exit problem.

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