Optimal control and the Fibonacci sequence

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Discussion Papers ; No. 674

Classification and Topics

• Classification: Wirtschaft
• Subject: Fibonacci sequence ; Golden ratio ; Mathematical number theory ; Optimal control.

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): von Brasch, Thomas ; Byström, Johan ; Lystad, Lars Petter
• Event: Veröffentlichung
• (who): Statistics Norway, Research Department
• (where): Oslo
• (when): 2012

Further information

• Handle: http://hdl.handle.net/10419/192656
• Last update: 10.03.2025, 11:43 AM CET