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Dynamic Optimal Choice When Rewards are Unbounded Below

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  • Qingyin Ma
  • John Stachurski

Abstract

We propose a new approach to solving dynamic decision problems with rewards that are unbounded below. The approach involves transforming the Bellman equation in order to convert an unbounded problem into a bounded one. The major advantage is that, when the conditions stated below are satisfied, the transformed problem can be solved by iterating with a contraction mapping. While the method is not universal, we show by example that many common decision problems do satisfy our conditions.

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  • Qingyin Ma & John Stachurski, 2019. "Dynamic Optimal Choice When Rewards are Unbounded Below," Papers 1911.13025, arXiv.org.
    • Handle: RePEc:arx:papers:1911.13025
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    1. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
    2. Greg Kaplan & Giovanni L. Violante, 2010. "How Much Consumption Insurance beyond Self-Insurance?," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(4), pages 53-87, October.
    3. 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.
    4. Jonathan Heathcote & Kjetil Storesletten & Giovanni L. Violante, 2010. "The Macroeconomic Implications of Rising Wage Inequality in the United States," Journal of Political Economy, University of Chicago Press, vol. 118(4), pages 681-722, August.
    5. Andreas Fagereng & Luigi Guiso & Davide Malacrino & Luigi Pistaferri, 2020. "Heterogeneity and Persistence in Returns to Wealth," Econometrica, Econometric Society, vol. 88(1), pages 115-170, January.
    6. Dan Cao, 2018. "Recursive Equilibrium in Krusell and Smith (1998)," Working Papers gueconwpa~18-18-13, Georgetown University, Department of Economics.
    7. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September.
    8. J. J. McCall, 1970. "Economics of Information and Job Search," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 84(1), pages 113-126.
    9. Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, vol. 50(2), pages 326-345, April.
    10. Aguiar, Mark & Amador, Manuel, 2019. "A contraction for sovereign debt models," Journal of Economic Theory, Elsevier, vol. 183(C), pages 842-875.
    11. Cristina Arellano, 2008. "Default Risk and Income Fluctuations in Emerging Economies," American Economic Review, American Economic Association, vol. 98(3), pages 690-712, June.
    12. V. Filipe Martins-da-Rocha & Yiannis Vailakis, 2010. "Existence and Uniqueness of a Fixed Point for Local Contractions," Econometrica, Econometric Society, vol. 78(3), pages 1127-1141, May.
    13. Jovanovic, Boyan, 1982. "Selection and the Evolution of Industry," Econometrica, Econometric Society, vol. 50(3), pages 649-670, May.
    14. Li, Huiyu & Stachurski, John, 2014. "Solving the income fluctuation problem with unbounded rewards," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 353-365.
    15. Benhabib, Jess & Bisin, Alberto & Zhu, Shenghao, 2015. "The wealth distribution in Bewley economies with capital income risk," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 489-515.
    16. Cuong Le Van & Yiannis Vailakis, 2005. "Recursive utility and optimal growth with bounded or unbounded returns," Post-Print halshs-00101201, HAL.
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