On an irreversible investment problem with two-factor uncertainty

Abstract

We consider a real options model for the optimal irreversible investment problem of a profit-maximizing company. The company has the opportunity to invest in 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.

Keywords:

• Real options
• Irreversible investment
• Optimal stopping
• Nonlinear integral equation
• Comparative statics

JEL Classification:

• G11
• C61
• D24

Acknowledgments

The authors thank two anonymous Referees for pertinent and useful comments on a first version of this work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) [grant number SFB 1283/2 2021-317210226].