IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v87y2024i3d10.1007_s10589-021-00278-3.html
   My bibliography  Save this article

Policy iteration for Hamilton–Jacobi–Bellman equations with control constraints

Author

Listed:
  • Sudeep Kundu

    (University of Graz)

  • Karl Kunisch

    (University of Graz
    Radon Institute for Computational and Applied Mathematics (RICAM))

Abstract

Policy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control theory. Its convergence analysis has attracted much attention in the unconstrained case. Here we analyze the case with control constraints both for the HJB equations which arise in deterministic and in stochastic control cases. The linear equations in each iteration step are solved by an implicit upwind scheme. Numerical examples are conducted to solve the HJB equation with control constraints and comparisons are shown with the unconstrained cases.

Suggested Citation

  • Sudeep Kundu & Karl Kunisch, 2024. "Policy iteration for Hamilton–Jacobi–Bellman equations with control constraints," Computational Optimization and Applications, Springer, vol. 87(3), pages 785-809, April.
    • Handle: RePEc:spr:coopap:v:87:y:2024:i:3:d:10.1007_s10589-021-00278-3
    DOI: 10.1007/s10589-021-00278-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-021-00278-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-021-00278-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lions & Benjamin Moll, 2017. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," NBER Working Papers 23732, National Bureau of Economic Research, Inc.
    2. Fei-Yue Wang & George N. Saridis, 2002. "On Successive Approximation of Optimal Control of Stochastic Dynamic Systems," International Series in Operations Research & Management Science, in: Moshe Dror & Pierre L’Ecuyer & Ferenc Szidarovszky (ed.), Modeling Uncertainty, chapter 0, pages 333-358, Springer.
    Full references (including those not matched with items on IDEAS)

    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. Deniz Sevinc & Edgar Mata Flores & Simon Collinson, 2020. "Are there inequality spillovers? Evidence through a modified inequality measure and European dynamics of inequality," Working Papers 545, ECINEQ, Society for the Study of Economic Inequality.
    2. Juan Carlos Parra-Alvarez & Olaf Posch & Mu-Chun Wang, 2017. "Estimation of Heterogeneous Agent Models: A Likelihood Approach," CESifo Working Paper Series 6717, CESifo.
    3. Niko Jaakkola & Florian Wagener, 2020. "All symmetric equilibria in differential games with public goods," Tinbergen Institute Discussion Papers 20-020/II, Tinbergen Institute.
    4. Bayer, Christian & Rendall, Alan D. & Wälde, Klaus, 2019. "The invariant distribution of wealth and employment status in a small open economy with precautionary savings," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 17-37.
    5. Likai Chen & Ekaterina Smetanina & Wei Biao Wu, 2022. "Estimation of nonstationary nonparametric regression model with multiplicative structure [Income and wealth distribution in macroeconomics: A continuous-time approach]," The Econometrics Journal, Royal Economic Society, vol. 25(1), pages 176-214.
    6. Sushant Acharya & Keshav Dogra, 2020. "Understanding HANK: Insights From a PRANK," Econometrica, Econometric Society, vol. 88(3), pages 1113-1158, May.
    7. Toda, Alexis Akira, 2019. "Wealth distribution with random discount factors," Journal of Monetary Economics, Elsevier, vol. 104(C), pages 101-113.
    8. Khieu, Hoang & Wälde, Klaus, 2023. "Capital income risk and the dynamics of the wealth distribution," Economic Modelling, Elsevier, vol. 122(C).
    9. Beatriz González & Galo Nuño & Dominik Thaler & Silvia Albrizio, 2021. "Firm heterogeneity, capital misallocation and optimal monetary policy," Working Papers 2145, Banco de España.
    10. Jesús Fernández‐Villaverde & Samuel Hurtado & Galo Nuño, 2023. "Financial Frictions and the Wealth Distribution," Econometrica, Econometric Society, vol. 91(3), pages 869-901, May.
    11. Adrien Auclert & Bence Bardóczy & Matthew Rognlie & Ludwig Straub, 2021. "Using the Sequence‐Space Jacobian to Solve and Estimate Heterogeneous‐Agent Models," Econometrica, Econometric Society, vol. 89(5), pages 2375-2408, September.
    12. Papp, Tamás K. & Reiter, Michael, 2020. "Estimating linearized heterogeneous agent models using panel data," Journal of Economic Dynamics and Control, Elsevier, vol. 115(C).
    13. Galo Nuño & Carlos Thomas, 2020. "Optimal Monetary Policy with Heterogeneous Agents," CESifo Working Paper Series 8670, CESifo.
    14. Frédéric Dufourt & Lisa Kerdelhué & Océane Piétri, 2022. "Budget-Neutral Capital Tax Cuts," Annals of Economics and Statistics, GENES, issue 146, pages 93-121.
    15. Saki Bigio & Yuliy Sannikov, 2019. "A Model of Intermediation, Money, Interest, and Prices," Working Papers 150, Peruvian Economic Association.
    16. Albertini, Julien & Fairise, Xavier & Terriau, Anthony, 2021. "Health, wealth, and informality over the life cycle," Journal of Economic Dynamics and Control, Elsevier, vol. 129(C).
    17. Facundo Piguillem & Loris Rubini, 2021. "Do non‐exporters lose from lower trade costs?," Review of International Economics, Wiley Blackwell, vol. 29(5), pages 1161-1185, November.
    18. Pietro Dindo & Andrea Modena & Loriana Pelizzon, 2019. "Risk Pooling, Leverage, and the Business Cycle," Working Papers 2019: 21, Department of Economics, University of Venice "Ca' Foscari".
    19. Alfonso A. Irarrazabal & Lin Ma & Juan Carlos Parra-Alvarez, 2023. "Optimal asset allocation for commodity sovereign wealth funds," Quantitative Finance, Taylor & Francis Journals, vol. 23(3), pages 471-495, March.
    20. Escudé, Matteo & Sinander, Ludvig, 2023. "Slow persuasion," Theoretical Economics, Econometric Society, vol. 18(1), January.
      • Matteo Escud'e & Ludvig Sinander, 2019. "Slow persuasion," Papers 1903.09055, arXiv.org, revised Apr 2022.

    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:spr:coopap:v:87:y:2024:i:3:d:10.1007_s10589-021-00278-3. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.