Some notes on discount factor restrictions for dynamic optimization problems
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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- Tapan Mitra & Gerhard Sorger, 1999. "Rationalizing Policy Functions by Dynamic Optimization," Econometrica, Econometric Society, vol. 67(2), pages 375-392, March.
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- Medio,Alfredo & Lines,Marji, 2001. "Nonlinear Dynamics," Cambridge Books, Cambridge University Press, number 9780521558747, October.
- 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.
- Medio,Alfredo & Lines,Marji, 2001. "Nonlinear Dynamics," Cambridge Books, Cambridge University Press, number 9780521551861, October.
- 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. Full references (including those not matched with items on IDEAS)
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