Contraction Mappings in the Theory Underlying Dynamic Programming

Denardo, Eric V.

doi:10.1137/1009030

Cited by 404 publications

(134 citation statements)

References 11 publications

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“…Since capital is bounded above byB, by standard arguments there exists a unique function v(x) in the space of bounded continuous functions on X satisfying the functional equation (15), and there also exist the corresponding optimal decision rules (see respectively Theorem 9.6 in Stokey and Lucas (1989) and Corollary 2 in Denardo (1967)). The proofs for R1 to R3 use these facts and follow from the same arguments as in Huggett 1993 (p. 964-68) and1997 (p. 399-400).…”

Section: Proof Of Remarksmentioning

confidence: 99%

Incomplete markets, labor supply and capital accumulation

Marcet

Obiols-Homs

Weil

2007

Journal of Monetary Economics

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We explore the accumulation of capital in the presence of limited insurance against idiosyncratic shocks, borrowing constraints and endogenous labor supply. In the exogenous labor supply case (e.g. Aiyagari 1994, Huggett 1997, the presence of limited insurance increases the demand for savings for precautionary reasons. As a consequence, capital and output are higher under incomplete markets. We show that if labor hours are endogenous, labor supply is likely to be lower under incomplete markets, because those agents who experience a high shock to productivity are ex post richer and they work fewer hours. In some cases, this wealth effect can overcome the "aggregate precautionary savings" and give rise to lower savings and output under incomplete markets.

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Section: Proof Of Remarksmentioning

confidence: 99%

Incomplete markets, labor supply and capital accumulation

Marcet

Obiols-Homs

Weil

2007

Journal of Monetary Economics

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“…for each a, r 1 , r 2 and some β ∈ (0, 1) (see Denardo (1967); Lucas and Stokey (1984); Stokey et al (1989).…”

Section: Introductionmentioning

confidence: 99%

Persistently Optimal Policies in Stochastic Dynamic Programming with Generalized Discounting

2013

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In this paper we study a Markov decision process with a non-linear discount function. Our approach is in spirit of the von Neumann-Morgenstern concept and is based on the notion of expectation. First, we define a utility on the space of trajectories of the process in the finite and infinite time horizon and then take their expected values. It turns out that the associated optimization problem leads to a non-stationary dynamic programming and an infinite system of Bellman equations, which result in obtaining persistently optimal policies. Our theory is enriched by examples.

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“…In case of unbounded instanteneous utility functions, one must combine this principle with a weighted norm approach, see Becker and Boyd III (1997) ;Boyd III (2006); Hernández-Lerma and Lasserre (1999). A construction of recursive utilities with the aid of the Banach Contraction Principle has been commenced by Denardo (1967), Lucas and Stokey (1984) and further developed in Becker and Boyd III (1997) ;Boyd III (2006); ? ); Marinacci and Montrucchio (2010) and references therein.…”

Section: Introductionmentioning

confidence: 99%