# On temporal aggregators and dynamic programming

Research Article

First Online:

- 138 Downloads
- 2 Citations

## Abstract

This paper proposes dynamic programming tools for payoffs based on aggregating functions that depend on the current action and the future expected payoff. Some regularity properties are provided on the aggregator to establish existence, uniqueness and computation of the solution to the Bellman equation. Our setting allows to encompass and generalize many previous results based upon additive or non-additive payoff functions.

## Keywords

Dynamic programming Temporal aggregators Intertemporal choice## JEL Classification

C61 D90## References

- Alvarez, F., Stokey, N.: Dynamic programming with homogeneous functions. J. Econ. Theory
**82**, 167–189 (1998)CrossRefGoogle Scholar - Becker, R.A., Boyd, J. III.: Capital Theory, Equilibrum Analysis and Recursive Utility. Blackwell, Hoboken (1997)Google Scholar
- Boyd, J. III.: Recursive utility and the Ramsey problem. J. Econ. Theory
**50**, 326–345 (1990)Google Scholar - Duran, J.: On dynamic programming with unbounded returns. Econ. Theory
**15**, 339–352 (2000)CrossRefGoogle Scholar - Jaśkiewicz, A., Matkowski, J., Nowak, A.S.: On variable discounting in dynamic programming: applications to resource extraction and other economic models. Ann. Oper. Res.
**220**, 263–278 (2014)CrossRefGoogle Scholar - Kamihigashi, T.: Elementary results on solutions to the Bellman equation of dynamic programming: existence, uniqueness and convergence. Econ. Theory
**56**, 251–273 (2014)CrossRefGoogle Scholar - Koopmans, T.: Stationary ordinal utility and impatience. Econometrica
**28**, 287–309 (1960)CrossRefGoogle Scholar - Le Van, C., Morhaim, L.: Optimal growth models with bounded or unbounded returns: a unifying approach. J. Econ. Theory
**105**, 158–187 (2002)CrossRefGoogle Scholar - Le Van, C., Vailakis, Y.: Recursive utility and optimal growth with bounded or unbounded returns. J. Econ. Theory
**123**, 187–209 (2005)CrossRefGoogle Scholar - Marinacci, M., Montrucchio, L.: Unique solutions for stochastic recursive utilities. J. Econ. Theory
**145**, 1776–1804 (2010)CrossRefGoogle Scholar - Martins-da-Rocha, V.F., Vailakis, Y.: Existence and uniqueness of a fixed point for local contractions. Econometrica
**78**, 1127–1141 (2010)CrossRefGoogle Scholar - Rincon-Zapatero, J.P., Rodriguez-Palmero, C.: Existence and uniqueness of solutions to the Belllman equation in the unbounded case. Econometrica
**71**, 1519–1555 (2003)CrossRefGoogle Scholar - Stokey, N., Lucas, R.E.: Optimal growth with many consumers. J. Econ. Theory
**32**, 139–171 (1984)CrossRefGoogle Scholar - Stokey, N., Lucas, R.E., Prescott, E.: Recursive Methods in Economic Dynamics. Harvard University Press, Cambridge (1989)Google Scholar
- Streufert, P.A.: Stationary recursive utility and dynamic programming under the assumption of biconvergence. Rev. Econ. Stud.
**57**, 79–97 (1990)CrossRefGoogle Scholar - Streufert, P.A.: An abstract topological approach to dynamic programming. J. Math. Econ.
**21**, 59–88 (1992)CrossRefGoogle Scholar - Yao, M.: Recursive utility and the solution to the Bellman equation, manuscript, Keio university, No. DP2016-08 (2016)Google Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 2017