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Optimal control and the Fibonacci sequence
Research Department, Unit for Macroeconomics, Statistics Norway.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Department of Technology, Narvik University College.
2012 (English)In: Journal of Optimization Theory and Applications, ISSN 0022-3239, E-ISSN 1573-2878, Vol. 154, no 3, p. 857-878Article in journal (Refereed) Published
Abstract [en]

We bridge mathematical number theory with 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

Place, publisher, year, edition, pages
2012. Vol. 154, no 3, p. 857-878
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-7420DOI: 10.1007/s10957-012-0061-2ISI: 000307438500008Scopus ID: 2-s2.0-84865418818Local ID: 5cc305d1-3540-44e0-961c-1a41e78d4969OAI: oai:DiVA.org:ltu-7420DiVA, id: diva2:980309
Note
Validerad; 2012; 20120430 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Byström, Johan

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