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Some notes on discount factor restrictions for dynamic optimization problems

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  • Sorger, Gerhard

Abstract

We consider dynamic optimization problems on one-dimensional state spaces. Under standard smoothness and convexity assumptions, the optimal solutions are characterized by an optimal policy function h mapping the state space into itself. There exists an extensive literature on the relation between the size of the discount factor of the dynamic optimization problem on the one hand and the properties of the dynamical system xt+1=h(xt) on the other hand. The purpose of this paper is to survey some of the most important contributions of this literature and to modify or improve them in various directions. We deal in particular with the topological entropy of the dynamical system, with its Lyapunov exponents, and with its periodic orbits.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 45 (2009)
Issue (Month): 7-8 (July)
Pages: 435-448

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Handle: RePEc:eee:mateco:v:45:y:2009:i:7-8:p:435-448

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Web page: http://www.elsevier.com/locate/jmateco

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Keywords: Dynamic optimization Discounting Topological entropy Lyapunov exponents Periodic orbits;

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References

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  1. Gerhard SORGER, 1992. "On the Sensitivity of Optimal Growth Paths," Vienna Economics Papers vie9202, University of Vienna, Department of Economics.
  2. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-82, September.
  3. Tapan Mitra & Gerhard Sorger, 1999. "Rationalizing Policy Functions by Dynamic Optimization," Econometrica, Econometric Society, vol. 67(2), pages 375-392, March.
  4. Mitra, Tapan, 1996. "An Exact Discount Factor Restriction for Period-Three Cycles in Dynamic Optimization Models," Journal of Economic Theory, Elsevier, vol. 69(2), pages 281-305, May.
  5. Montrucchio, Luigi & Sorger, Gerhard, 1996. "Topological entropy of policy functions in concave dynamic optimization models," Journal of Mathematical Economics, Elsevier, vol. 25(2), pages 181-194.
  6. Nishimura, Kazuo & Yano, Makoto, 1996. "On the Least Upper Bound of Discount Factors That Are Compatible with Optimal Period-Three Cycles," Journal of Economic Theory, Elsevier, vol. 69(2), pages 306-333, May.
  7. Mitra, Tapan, 1998. "On the relationship between discounting and complicated behavior in dynamic optimization models," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 421-434, January.
  8. Medio,Alfredo & Lines,Marji, 2001. "Nonlinear Dynamics," Cambridge Books, Cambridge University Press, number 9780521551861, April.
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