Optimal control and the Fibonacci sequence

Thomas von Brasch, Johan Byström and Lars Petter Lystad ()
Additional contact information
Lars Petter Lystad: Statistics Norway, https://www.ssb.no/en/forskning/ansatte

Discussion Papers from Statistics Norway, Research Department

Abstract: 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.

Keywords: Fibonacci sequence; Golden ratio; Mathematical number theory; Optimal control. (search for similar items in EconPapers)
JEL-codes: C6 (search for similar items in EconPapers)
Date: 2012-01
New Economics Papers: this item is included in nep-dge and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.ssb.no/a/publikasjoner/pdf/DP/dp674.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ssb:dispap:674

Access Statistics for this paper

More papers in Discussion Papers from Statistics Norway, Research Department P.O.Box 8131 Dep, N-0033 Oslo, Norway. Contact information at EDIRC.
Bibliographic data for series maintained by L Maasø ().