Abstract
This chapter concerns deterministic and stochastic nonstationary discrete-time optimal control problems (OCPs) with an infinite horizon. We show, using Gâteaux differentials, that the so-called Euler equation (EE) and a transversality condition (TC) are necessary conditions for optimality. In particular, the TC is obtained in a more general form and under milder hypotheses than in previous works. Sufficient conditions are also provided. We find closed-form solutions to several (discounted) stationary and nonstationary control problems. The results in this chapter come from González–Sánchez and Hernández–Lerma [37].
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© 2013 David González-Sánchez and Onésimo Hernández-Lerma
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González-Sánchez, D., Hernández-Lerma, O. (2013). Direct Problem: The Euler Equation Approach. In: Discrete–Time Stochastic Control and Dynamic Potential Games. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-01059-5_2
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DOI: https://doi.org/10.1007/978-3-319-01059-5_2
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