Optimal control and the Fibonacci sequence
AbstractWe 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.
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Bibliographic InfoPaper provided by Research Department of Statistics Norway in its series Discussion Papers with number 674.
Date of creation: Jan 2012
Date of revision:
Fibonacci sequence; Golden ratio; Mathematical number theory; Optimal control.;
Find related papers by JEL classification:
- C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Modeling with Large Data Sets
- N40 - Economic History - - Government, War, Law, International Relations, and Regulation - - - General, International, or Comparative
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-02-01 (All new papers)
- NEP-DGE-2012-02-01 (Dynamic General Equilibrium)
- NEP-ORE-2012-02-01 (Operations Research)
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