Abstract
In this paper, we apply the idea of k-local contraction of Rincón-Zapatero and Rodriguez-Palmero (Econometrica 71:1519–1555, 2003; Econ Theory 33:381–391, 2007) to study discounted stochastic dynamic programming models with unbounded returns. Our main results concern the existence of a unique solution to the Bellman equation and are applied to the theory of stochastic optimal growth. Also a discussion of some subtle issues concerning k-local and global contractions is included.
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We wish to thank an associate editor and two referees for many constructive and helpful comments.
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Matkowski, J., Nowak, A.S. On discounted dynamic programming with unbounded returns. Econ Theory 46, 455–474 (2011). https://doi.org/10.1007/s00199-010-0522-5
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DOI: https://doi.org/10.1007/s00199-010-0522-5
Keywords
- Stochastic dynamic programming
- Bellman functional equation
- Contraction mapping
- Stochastic optimal growth