Robust optimal R&D investment under technical uncertainty in a regime-switching environment

ABSTRACT

In this paper, we extend the classic optimal research and development (R&D) investment model into the regime-switching environment. We formulate a robust model to obtain the maximal net value function of the R&D project under a family of real-world measures, which can also be regarded as a stochastic differential game. Then, the verification argument is provided. Though we do not find the closed-form solution, we give a numerical simulation to further study the qualities of the solution to our model.

Keywords:

• Regime-switching
• research and development
• HJBI equation
• change of measures

Mathematics Subject Classifications:

• 60J20
• 91A15
• 91B38
• 93C30
• 93E20

Acknowledgments

The authors are grateful to Professor G.-W. Weber, the editor and reviewers for their constructive comments, which helps us to improve the paper.

Disclosure statement

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

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11471230 and 11671282] and the Fundamental Research Funds for Central Universities [grant number 2012017yjsy142].