  We consider a real options model for the optimal irreversible investment
problem of a profit maximizing company. The company has the opportunity to
invest into a production plant capable of producing two products, of which the
prices follow two independent geometric Brownian motions. After paying a
constant sunk investment cost, the company sells the products on the market and
thus receives a continuous stochastic revenue-flow. This investment problem is
set as a two-dimensional optimal stopping problem. We find that the optimal
investment decision is triggered by a convex curve, which we characterize as
the unique continuous solution to a nonlinear integral equation. Furthermore,
we provide analytical and numerical comparative statics results of the
dependency of the project's value and investment decision with respect to the
model's parameters.
