We consider optimal selling rules for stocks and options pricing under a regime-switching model which consists of a set of geometric Brownian motions. We introduce two approaches to study the underlying problems. One approach is via viscosity solutions with numerical methods and the other is to find a closed-form solution. Finding a closed form solution isusually applicable in only limited cases. In this dissertation, we study four related topics.As the first, we consider two different ways to evaluate closed-form solutions of Americanput options whose underlying asset is governed by regime-switching model. Second, we useviscosity solutions to attain the optimal value function under a regime-switching model ofEuropean call options. Third, we apply the method to solve optimal selling rules to buyand-sell problem under an underlying asset governed by a mean-reverting model. As the lastpart of this dissertation, we consider an optimal selling rule for a large block of stocks undera regime-switching model.