In this article, a general form of optimal stopping problems in regime-switching models is studied under certain standard assumptions. An optimal stopping problem with an arbitrary value function in a two-regime environment can be reduced to a pair of optimal stopping problems without regime switching. A method for finding optimal stopping rules is proposed using the techniques available for non-switching problems. In contrast to other methods, our systematic solution procedure is more direct since we first obtain the explicit form of the value functions. In the end, we discuss a problem which may not be dealt with by the conventional methods, demonstrating the computational simplicity of our approach.
Pricing financial or real options with arbitrary payoffs in regime-switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in regime-switching models . In this article, we reduce an optimal stopping problem with an arbitrary value function in a two-regime environment to a pair of optimal stopping problems without regime switching. We then propose a method for finding optimal stopping rules using the techniques available for non-switching problems. In contrast to other methods, our systematic solution procedure is more direct since we first obtain the explicit form of the value functions. In the end, we discuss an option pricing problem which may not be dealt with by the conventional methods, demonstrating the simplicity of our approach.
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