Solution existence theorems for finite horizon optimal economic growth problems

Abstract

The solution existence of finite horizon optimal economic growth problems is studied by invoking Filippov's Existence Theorem for optimal control problems from the monograph of Cesari L. [Optimization theory and applications. New York: Springer-Verlag; 1983]. Our results are obtained not only for general problems but also for typical ones, where the production function is given by either the AK function or the Cobb–Douglas one, while the utility function can be in a linear or power form. Some open questions and conjectures about the regularity of global solutions of finite horizon optimal economic growth problems are formulated in this paper.

Keywords:

• Optimal economic growth
• optimal control
• finite horizon
• solution existence
• regularity

2010 Mathematics Subject Classifications:

• 91B62
• 49J15
• 37N40
• 46N10
• 91B55

Acknowledgments

This work was supported by the project ‘Some qualitative properties of optimization problems and dynamical systems, and applications’ (Code: ICRTM01$\mathrm{\_}$2020.08) of the International Center for Research and Postgraduate Training in Mathematics (ICRTM) under the auspices of UNESCO of Institute of Mathematics, Vietnam Academy of Science and Technology. The author would like to thank Professor Nguyen Dong Yen and the two anonymous referees for their valuable comments and suggestions on the earlier versions of the present paper.

Disclosure statement

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