Optimal control and the Fibonacci sequence
We bridge mathematical number theory with that of optimal control and show that a generalised Fibonacci sequence enters the control function of finite horizon dynamic optimisation problems with one state and one control variable. In particular, we show that the recursive expression describing the first-order approximation of the control function can be written in terms of a generalised Fibonacci sequence when restricting the final state to equal the steady state of the system. Further, by deriving the solution to this sequence, we are able to write the first-order approximation of optimal control explicitly. Our procedure is illustrated in an example often referred to as the Brock-Mirman economic growth model.
|Date of creation:||Jan 2012|
|Date of revision:|
|Contact details of provider:|| Postal: P.O.Box 8131 Dep, N-0033 Oslo, Norway|
Phone: (+47) 21 09 00 00
Fax: (+47) 21 09 49 73
Web page: http://www.ssb.no/en/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Magill, Michael J. P., 1977. "Some new results on the local stability of the process of capital accumulation," Journal of Economic Theory, Elsevier, vol. 15(1), pages 174-210, June.
- Levine, Paul & Pearlman, Joseph G. & Pierse, Richard, 2007.
"Linear-quadratic approximation, external habit and targeting rules,"
Working Paper Series
0759, European Central Bank.
- Levine, Paul & Pearlman, Joseph & Pierse, Richard, 2008. "Linear-quadratic approximation, external habit and targeting rules," Journal of Economic Dynamics and Control, Elsevier, vol. 32(10), pages 3315-3349, October.
- Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711.
- Magill, Michael J. P., 1977. "A local analysis of N-sector capital accumulation under uncertainty," Journal of Economic Theory, Elsevier, vol. 15(1), pages 211-219, June.
When requesting a correction, please mention this item's handle: RePEc:ssb:dispap:674. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (J Bruusgaard)
If references are entirely missing, you can add them using this form.