Entry-e*t decisions apply to numerous pra*ical problems. For example， wheto extra* oil and wheto stop the extra*ion， wheto issue a new policy and wheto end it， and wheto let a kind of produ* enter a *rket and wheto let the produ* e*t the *rket， etc. Therefore， entry-e*t decisioproblems *tra* a lot of researche*.
There are three approaches to study entry-e*t decisions， namely， real option， pure probability and opti*l stopping. Ithis monograph， we appeal to opti*l stopping to deal with entry-e*t decisions. The *ireasons are as follows. Othe one hand， ithe real optioframework， the regularity of payoff fun*ions is a priori assumed， while the opti*l stopping approach intends to prove it. Othe other hand， although the pure probability and opti*l stopping approaches are both to solve a opti*l stopping problem， we have to calcul*e density fun*ions of some stopping times if applying the pure probability approach， which is not easy， whereas the opti*l stopping one avoids such calcul*ions.
We aim to obtaiclosed-form solutions of opti*l entry-e*t decisions for the cases： costs depending ounderlying processes， implement*iowith delay， and underlying processes following geometric Levy processes. Iaddition， we provide a *plete theory for opti*l stopping problems with regime switching， and use it to solve ae*t problem.