IDEAS home Printed from https://ideas.repec.org/p/kyo/wpaper/617.html
   My bibliography  Save this paper

Stochastic Optimal Policies When the Discout Rate Vanishes

Author

Listed:
  • Kazuo Nishimura

    () (Institute of Economic Research, Kyoto University)

  • John Stachurski

    () (Department of Economics, University of Melbourne)

Abstract

Dutta (J. Econom. Theory, 1991, 55, 64?94) showed that long-run optimality of the limit of discounted optima when the discount rate vanishes is implied by a certain bound on the value function of the optimal program. We introduce a new method to verify this bound using coupling techniques.

Suggested Citation

  • Kazuo Nishimura & John Stachurski, 2006. "Stochastic Optimal Policies When the Discout Rate Vanishes," KIER Working Papers 617, Kyoto University, Institute of Economic Research.
  • Handle: RePEc:kyo:wpaper:617
    as

    Download full text from publisher

    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP617.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2008. "A qualitative approach to Markovian equilibrium in infinite horizon economies with capital," Journal of Economic Theory, Elsevier, vol. 139(1), pages 75-98, March.
    2. Danthine, Jean-Pierre & Donaldson, John B, 1981. "Stochastic Properties of Fast vs. Slow Growing Economies," Econometrica, Econometric Society, vol. 49(4), pages 1007-1033, June.
    3. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
    4. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-1406, November.
    5. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 11(3), pages 329-339, December.
    6. Dutta, Prajit K., 1991. "What do discounted optima converge to?: A theory of discount rate asymptotics in economic models," Journal of Economic Theory, Elsevier, vol. 55(1), pages 64-94, October.
    7. Rosenthal J.S., 2003. "Asymptotic Variance and Convergence Rates of Nearly-Periodic Markov Chain Monte Carlo Algorithms," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 169-177, January.
    8. Dutta, P.K., 1991. "What Do Discounted Optima Converge To? A Theory of Discount Rate Asymptotics in Economic Models," RCER Working Papers 264, University of Rochester - Center for Economic Research (RCER).
    9. Nishimura, Kazuo & Stachurski, John, 2005. "Stability of stochastic optimal growth models: a new approach," Journal of Economic Theory, Elsevier, vol. 122(1), pages 100-118, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kitti, Mitri, 2018. "Sustainable social choice under risk," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 19-31.
    2. A. Jaśkiewicz, 2009. "Zero-Sum Ergodic Semi-Markov Games with Weakly Continuous Transition Probabilities," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 321-347, May.
    3. Armando F. Mendoza-Pérez & Héctor Jasso-Fuentes & Omar A. De-la-Cruz Courtois, 2016. "Constrained Markov decision processes in Borel spaces: from discounted to average optimality," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(3), pages 489-525, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kazuo Nishimura & John Stachurski, 2004. "Stochastic Optimal Growth when the Discount Rate Vanishes," Department of Economics - Working Papers Series 908, The University of Melbourne.
    2. Olson, Lars J. & Roy, Santanu, 2005. "Theory of Stochastic Optimal Economic Growth," Working Papers 28601, University of Maryland, Department of Agricultural and Resource Economics.
    3. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, September.
    4. Datta, Manjira & Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2005. "Markovian equilibrium in infinite horizon economies with incomplete markets and public policy," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 505-544, August.
    5. Kazuo Nishimura & Ryszard Rudnicki & John Stachurski, 2004. "Stochastic Growth With Nonconvexities:The Optimal Case," Department of Economics - Working Papers Series 897, The University of Melbourne.
    6. Zhang, Yuzhe, 2007. "Stochastic optimal growth with a non-compact state space," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 115-129, February.
    7. Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2008. "A qualitative approach to Markovian equilibrium in infinite horizon economies with capital," Journal of Economic Theory, Elsevier, vol. 139(1), pages 75-98, March.
    8. Juan Pablo Rinc'on-Zapatero, 2019. "Existence and Uniqueness of Solutions to the Stochastic Bellman Equation with Unbounded Shock," Papers 1907.07343, arXiv.org.
    9. Nishimura, Kazuo & Rudnicki, Ryszard & Stachurski, John, 2006. "Stochastic optimal growth with nonconvexities," Journal of Mathematical Economics, Elsevier, vol. 42(1), pages 74-96, February.
    10. Manjira Datta & Leonard Mirman & Olivier Morand & Kevin Reffett, 2002. "Monotone Methods for Markovian Equilibrium in Dynamic Economies," Annals of Operations Research, Springer, vol. 114(1), pages 117-144, August.
    11. Cuong Van & John Stachurski, 2007. "Parametric continuity of stationary distributions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(2), pages 333-348, November.
    12. Cai, Yiyong & Kamihigashi, Takashi & Stachurski, John, 2014. "Stochastic optimal growth with risky labor supply," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 167-176.
    13. Gong, Liutang & Zhao, Xiaojun & Yang, Yunhong & Hengfu, Zou, 2010. "Stochastic growth with social-status concern: The existence of a unique stable distribution," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 505-518, July.
    14. Chatterjee, Partha & Shukayev, Malik, 2008. "Note on positive lower bound of capital in the stochastic growth model," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2137-2147, July.
    15. Takashi Kamihigashi & John Stachurski, 2014. "Stability Analysis for Random Dynamical Systems in Economics," Discussion Paper Series DP2014-35, Research Institute for Economics & Business Administration, Kobe University.
    16. Kamihigashi, Takashi & Stachurski, John, 2016. "Seeking ergodicity in dynamic economies," Journal of Economic Theory, Elsevier, vol. 163(C), pages 900-924.
    17. Leonard J. Mirman & Kevin Reffett & Marc Santugini, 2016. "On learning and growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(4), pages 641-684, April.
    18. Manjira Datta & Kevin L. Reffett, 2005. "Isotone Recursive Methods: the Case of Homogeneous Agents," Tinbergen Institute Discussion Papers 05-012/2, Tinbergen Institute.
    19. Jaime McGovern & Olivier Morand & Kevin Reffett, 2013. "Computing minimal state space recursive equilibrium in OLG models with stochastic production," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 623-674, November.
    20. Manjira Datta & Leonard Mirman & Kevin Reffett, "undated". "Nonclassical Brock-Mirman Economies," Working Papers 2179544, Department of Economics, W. P. Carey School of Business, Arizona State University.

    More about this item

    Keywords

    Dynamic programming; Long-run optimality.;

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kyo:wpaper:617. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ryo Okui) The email address of this maintainer does not seem to be valid anymore. Please ask Ryo Okui to update the entry or send us the correct email address. General contact details of provider: http://edirc.repec.org/data/iekyojp.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.