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

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.