A general framework for optimal stopping problems with two risk factors and real option applications

Abstract

A new explicit solution is obtained for a general class of two‐dimensional optimal stopping problems arising in real option theory. First, the solvable case of homogeneous and quasi‐homogeneous problems is presented in a comprehensive framework. Then the general problem—including the unsolved case of inhomogeneous functions—is considered and an explicit expression for the value function is obtained in terms of a modified Bessel function of second kind. Then we clarify the link between the general solution method and the more elementary one in the specific (quasi‐)homogeneous problem. Finally, this article provides some useful formulas and some insights for the one‐dimensional case as well.