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 nonswitching problems. In contrast to other methods, our systematic solution procedure is more direct as 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.

中文翻译：

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政权转换模型中价格选项的直接解决方法

在体制转换模型中对具有任意收益的金融或实物期权定价是金融中的一个重要问题。从数学上讲，这是在某些标准假设下解决体制转换模型中最优停止问题的一般形式。在本文中，我们将具有两个区域环境中的任意值函数的最优停止问题减少为一对无需体制转换的最优停止问题。然后，我们提出了一种使用可用于非切换问题的技术来找到最佳停止规则的方法。与其他方法相比，由于我们首先获得值函数的显式形式，因此系统的求解过程更加直接。最后，我们讨论了期权定价问题，这是传统方法可能无法解决的，证明了我们方法的简单性。