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Differentiability of the value function and Euler equation in non-concave discrete-time stochastic dynamic programming

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  • Juan Pablo Rincón-Zapatero

    (Universidad Carlos III de Madrid)

Abstract

We consider a stochastic, non-concave dynamic programming problem admitting interior solutions and prove, under mild conditions, that the expected value function is differentiable along optimal paths. This property allows us to obtain rigorously the Euler equation as a necessary condition of optimality for this class of problems.

Suggested Citation

  • Juan Pablo Rincón-Zapatero, 2020. "Differentiability of the value function and Euler equation in non-concave discrete-time stochastic dynamic programming," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 79-88, April.
    • Handle: RePEc:spr:etbull:v:8:y:2020:i:1:d:10.1007_s40505-019-00166-4
    DOI: 10.1007/s40505-019-00166-4
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    More about this item

    Keywords

    Dynamic programming; Euler equation; Envelope Theorem;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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