On the Principle of Optimality for Nonstationary Deterministic Dynamic Programming
This note studies a general nonstationary infinite-horizon optimization problem in discrete time. We allow the state space in each period to be an arbitrary set, and the return function in each period to be unbounded. We do not require discounting, and do not require the constraint correspondence in each period to be nonempty-valued. The objective function is defined as the limit superior or inferior of the finite sums of return functions. We show that the sequence of time-indexed value functions satisfies the Bellman equation if and only if its right-hand side is well defined, i.e., it does not involve -∞+∞.
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- Le Van, C. & Morhaim, L., 2000.
"Optimal Growth Models with Bounded or Unbounded Returns : a Unifying Approach,"
Papiers d'Economie MathÃ©matique et Applications
2000.64, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
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- repec:dau:papers:123456789/433 is not listed on IDEAS
- Juan Pablo RincÛn-Zapatero & Carlos RodrÌguez-Palmero, 2003. "Existence and Uniqueness of Solutions to the Bellman Equation in the Unbounded Case," Econometrica, Econometric Society, vol. 71(5), pages 1519-1555, 09.
- Michel, Philippe, 1990. "Some Clarifications on the Transversality Condition," Econometrica, Econometric Society, vol. 58(3), pages 705-23, May.
- McKenzie, Lionel W., 2005. "Optimal economic growth, turnpike theorems and comparative dynamics," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 2, volume 3, chapter 26, pages 1281-1355 Elsevier.
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