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Necessary and Sufficient Conditions for a Solution of the Bellman Equation to be the Value Function: A General Principle

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Abstract

In this paper, we give Necessary and Sufficient Conditions for a Solution of the Belman Equation to be the Value Function. This result is a general principle. It requires no structure beyond the common framework of discrete-time stationary optimization problems with time-additive returns. In particular, the state space X is an arbitrary set

Suggested Citation

  • Takashi Kamihigashi & Cuong Le Van, 2015. "Necessary and Sufficient Conditions for a Solution of the Bellman Equation to be the Value Function: A General Principle," Documents de travail du Centre d'Economie de la Sorbonne 15007, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:15007
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    2. Le Van, Cuong & Morhaim, Lisa, 2002. "Optimal Growth Models with Bounded or Unbounded Returns: A Unifying Approach," Journal of Economic Theory, Elsevier, vol. 105(1), pages 158-187, July.
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    6. V. Filipe Martins-da-Rocha & Yiannis Vailakis, 2010. "Existence and Uniqueness of a Fixed Point for Local Contractions," Econometrica, Econometric Society, vol. 78(3), pages 1127-1141, May.
    7. Takashi Kamihigashi, 2008. "On the principle of optimality for nonstationary deterministic dynamic programming," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(4), pages 519-525, December.
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    More about this item

    Keywords

    Dynamic programming; Bellman equation; value function; fixed point;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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