Monotone Concave Operators: An application to the existence and uniqueness of solutions to the Bellman equation
We propose a new approach to the issue of existence and uniqueness of solutions to the Bellman equation, exploiting an emerging class of methods, called monotone map methods, pioneered in the work of Krasnosel'skii-Zabreiko (1984). The approach is technically simple and intuitive. It is derived from geometric ideas related to the study of fixed points for monotone concave operators defined on partially order spaces.
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- Le Van, Cuong & Vailakis, Yiannis, 2005.
"Recursive utility and optimal growth with bounded or unbounded returns,"
Journal of Economic Theory,
Elsevier, vol. 123(2), pages 187-209, August.
- LE VAN, Cuong & VAILAKIS, Yiannis, 2002. "Recursive utility and optimal growth with bounded or unbounded returns," CORE Discussion Papers 2002055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Kennan,J., 2001.
"Uniqueness of positive fixed points for increasing concave functions on Rn : an elementary result,"
2, Wisconsin Madison - Social Systems.
- John Kennan, 2001. "Uniqueness of Positive Fixed Points for Increasing Concave Functions on Rn: An Elementary Result," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(4), pages 893-899, October.
- Juan Pablo RincÛn-Zapatero & Carlos RodrÌguez-Palmero, 2003. "Existence and Uniqueness of Solutions to the Bellman Equation in the Unbounded Case," Econometrica, Econometric Society, vol. 71(5), pages 1519-1555, 09.
- Duran, Jorge, 1997.
"On dynamic programming with unbounded returns,"
CEPREMAP Working Papers (Couverture Orange)
- Duran, Jorge, 1997. "On Dynamic Programming with Unbounded Returns," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 1997033, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
- Morand, Olivier F. & Reffett, Kevin L., 2003.
"Existence and uniqueness of equilibrium in nonoptimal unbounded infinite horizon economies,"
Journal of Monetary Economics,
Elsevier, vol. 50(6), pages 1351-1373, September.
- Olivier F. Morand & Kevin L. Reffett, 2001. "Existence and Uniqueness of Equilibrium in Nonoptimal Unbounded Infinite Horizon Economies," Working papers 2001-02, University of Connecticut, Department of Economics.
- Manjira Datta & Leonard Mirman & Kevin Reffett, .
"Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor,"
2132846, Department of Economics, W. P. Carey School of Business, Arizona State University.
- Datta, Manjira & Mirman, Leonard J. & Reffett, Kevin L., 2002. "Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor," Journal of Economic Theory, Elsevier, vol. 103(2), pages 377-410, April.
- Wilbur John Coleman II, 1989.
"Equilibrium in a production economy with an income tax,"
International Finance Discussion Papers
366, Board of Governors of the Federal Reserve System (U.S.).
- Coleman, Wilbur John, II, 1991. "Equilibrium in a Production Economy with an Income Tax," Econometrica, Econometric Society, vol. 59(4), pages 1091-1104, July.
- Streufert, Peter A, 1990. "Stationary Recursive Utility and Dynamic Programming under the Assumption of Biconvergence," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 79-97, January.
- Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, vol. 50(2), pages 326-345, April.
- Coleman, Wilbur II, 2000. "Uniqueness of an Equilibrium in Infinite-Horizon Economies Subject to Taxes and Externalities," Journal of Economic Theory, Elsevier, vol. 95(1), pages 71-78, November.
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