Discussion Papers no. 674

Optimal control and the Fibonacci sequence

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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.

Om publikasjonen

Tittel

Optimal control and the Fibonacci sequence

Ansvarlige

Thomas von Brasch, Johan Byström, Terje Skjerpen

Serie og -nummer

Discussion Papers no. 674

Utgiver

Statistics Norway

Emne

Discussion Papers

ISSN

1892-753X

Antall sider

33

Målform

Engelsk

Om Discussion Papers

Discussion papers comprise research papers intended for international journals and books. A preprint of a Discussion Paper may be longer and more elaborate than a standard journal article as it may include intermediate calculations, background material etc.

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