IDEAS home Printed from https://ideas.repec.org/a/bpj/maecol/v1y2014i2-4p8n2.html
   My bibliography  Save this article

Optimal Control Problems with State Specific Jumps in the State Equation

Author

Listed:
  • Caliendo Frank N.

    (Utah State University, USA)

  • Guo Nick L.

    (Utah State University, USA)

Abstract

An important class of control problems in economics are those in which the state equation switches (jumps) whenever the state variable crosses a threshold. An example is a life-cycle problem in which a household faces higher rates on borrowing than on lending, and therefore the interest rate on the household's asset balance switches discretely each time the asset balance switches signs [6]. The existing method for solving such a problem is notoriously difficult to compute because the first-order conditions include a continuum of complementary slackness conditions. In this paper we provide an easy solution method that utilizes the standard Maximum Principle for unconstrained optimization problems. No inequality constraints (and therefore no complementary slackness conditions) are required.

Suggested Citation

  • Caliendo Frank N. & Guo Nick L., 2014. "Optimal Control Problems with State Specific Jumps in the State Equation," Mathematical Economics Letters, De Gruyter, vol. 1(2-4), pages 61-68, July.
    • Handle: RePEc:bpj:maecol:v:1:y:2014:i:2-4:p:8:n:2
    DOI: 10.1515/mel-2013-0005
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/mel-2013-0005
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/mel-2013-0005?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. Markus K. Brunnermeier & Yuliy Sannikov, 2014. "A Macroeconomic Model with a Financial Sector," American Economic Review, American Economic Association, vol. 104(2), pages 379-421, February.
    2. Boucekkine, Raouf & Saglam, Cagri & Valléee, Thomas, 2004. "Technology Adoption Under Embodiment: A Two-Stage Optimal Control Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 8(2), pages 250-271, April.
    3. Ngo Van Long & Koji Shimomura, 2003. "A new proof of the maximum principle," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(3), pages 671-674, October.
    4. Markus K. Brunnermeier & Thomas M. Eisenbach & Yuliy Sannikov, 2012. "Macroeconomics with Financial Frictions: A Survey," Levine's Working Paper Archive 786969000000000384, David K. Levine.
    5. David Laibson & Andrea Repetto & Jeremy Tobacman, 2005. "Estimating Discount Functions with Consumption Choices over the Lifecycle," Levine's Bibliography 784828000000000643, UCLA Department of Economics.
    6. Gertler, Mark & Kiyotaki, Nobuhiro, 2010. "Financial Intermediation and Credit Policy in Business Cycle Analysis," Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 11, pages 547-599, Elsevier.
    7. Léonard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521331586, January.
    8. repec:bla:ecorec:v:53:y:1977:i:142&143:p:405-20 is not listed on IDEAS
    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. Hans Gersbach & Jean-Charles Rochet & Martin Scheffel, 2023. "Financial Intermediation, Capital Accumulation, and Crisis Recovery," Review of Finance, European Finance Association, vol. 27(4), pages 1423-1469.
    2. Cuong Le Van & Ngoc-Sang Pham, 2016. "Intertemporal equilibrium with financial asset and physical capital," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 155-199, June.
    3. Ai, Hengjie & Li, Kai & Yang, Fang, 2020. "Financial intermediation and capital reallocation," Journal of Financial Economics, Elsevier, vol. 138(3), pages 663-686.
    4. Suh, Hyunduk & Walker, Todd B., 2016. "Taking financial frictions to the data," Journal of Economic Dynamics and Control, Elsevier, vol. 64(C), pages 39-65.
    5. Hamed Ghiaie, 2018. "Shadow Bank run, Housing and Credit Market: The Story of a Recession," THEMA Working Papers 2018-01, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    6. Marco Maffezzoli & Tommaso Monacelli, 2015. "Deleverage and Financial Fragility," Working Papers 546, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    7. Ferrari, Massimo, 2014. "The financial meltdown: a model with endogenous default probability," MPRA Paper 59419, University Library of Munich, Germany.
    8. David Martinez‐Miera & Rafael Repullo, 2017. "Search for Yield," Econometrica, Econometric Society, vol. 85, pages 351-378, March.
    9. Kargar, Mahyar, 2021. "Heterogeneous intermediary asset pricing," Journal of Financial Economics, Elsevier, vol. 141(2), pages 505-532.
    10. Hu, Weiping & Li, Kai & Zhang, Xiao, 2024. "Financial constraints, cash flow timing patterns, and asset prices," Journal of Financial Economics, Elsevier, vol. 157(C).
    11. Luigi Bocola, 2016. "The Pass-Through of Sovereign Risk," Journal of Political Economy, University of Chicago Press, vol. 124(4), pages 879-926.
    12. Hengjie Ai & Jun E Li & Kai Li & Christian Schlag, 2020. "The Collateralizability Premium," The Review of Financial Studies, Society for Financial Studies, vol. 33(12), pages 5821-5855.
    13. Kai Li & Jun Li & Christian Schlag & Hengjie Ai, 2017. "Asset Collateralizability and the Cross-Section of Expected Returns," 2017 Meeting Papers 1029, Society for Economic Dynamics.
    14. Beck, Thorsten & Colciago, Andrea & Pfajfar, Damjan, 2014. "The role of financial intermediaries in monetary policy transmission," Journal of Economic Dynamics and Control, Elsevier, vol. 43(C), pages 1-11.
    15. Narcissa Balta & Bořek Vašíček, 2020. "Financial channels and economic activity in the euro area: a large-scale Bayesian VAR approach," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 47(2), pages 431-451, May.
    16. Hu, Weiwei & Li, Kai & Xu, Yiming, 2023. "Leasing and the allocation efficiency of finance," Journal of Empirical Finance, Elsevier, vol. 74(C).
    17. Christian Bittner & Diana Bonfim & Florian Heider & Farzad Saidi & Glenn Schepens & Carla Soares, 2022. "The Augmented Bank Balance-Sheet Channel of Monetary Policy," ECONtribute Discussion Papers Series 149, University of Bonn and University of Cologne, Germany.
    18. Alessandri, Piergiorgio & Mumtaz, Haroon, 2019. "Financial regimes and uncertainty shocks," Journal of Monetary Economics, Elsevier, vol. 101(C), pages 31-46.
    19. Hans Gersbach & Jean-Charles Rochet & Martin Scheffel, 2016. "Taking Banks to Solow," International Economic Association Series, in: Joseph E. Stiglitz & Martin Guzman (ed.), Contemporary Issues in Macroeconomics, chapter 13, pages 176-198, Palgrave Macmillan.
    20. Tobias Adrian & Nellie Liang, 2018. "Monetary Policy, Financial Conditions, and Financial Stability," International Journal of Central Banking, International Journal of Central Banking, vol. 14(1), pages 73-131, January.

    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:bpj:maecol:v:1:y:2014:i:2-4:p:8:n:2. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.