IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v91y2018icp369-390.html
   My bibliography  Save this article

Classical and restricted impulse control for the exchange rate under a stochastic trend model

Author

Listed:
  • Runggaldier, Wolfgang J.
  • Yasuda, Kazuhiro

Abstract

Building on Cadenillas and Zapatero (2000) and Bertola et al. (2016) we consider the problem faced by a Central Bank to optimally control the exchange rate, whereby the control is composed of a direct impulse control intervention and an indirect, continuously acting intervention given by the control of the domestic interest rate. Similarly to Cadenillas and Zapatero (2000) and Bertola et al. (2016) we formulate the problem as a mixed classical-impulse control problem and the approach is based on a quasi-variational inequality by considering a specific class of the optimal value functions and controls. As in Bertola et al. (2016), but differently from Cadenillas and Zapatero (2000), we consider a finite horizon that makes the problem time inhomogeneous and we do not have to impose a smooth fit condition so that a fully analytical solution is possible. With respect to Bertola et al. (2016) we generalize the problem by letting, more realistically, the drift in the dynamics of the exchange rate to be time varying or even unobservable so that it has to be filter-estimated from observable data. Numerical illustrations are presented as well.

Suggested Citation

  • Runggaldier, Wolfgang J. & Yasuda, Kazuhiro, 2018. "Classical and restricted impulse control for the exchange rate under a stochastic trend model," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 369-390.
  • Handle: RePEc:eee:dyncon:v:91:y:2018:i:c:p:369-390
    DOI: 10.1016/j.jedc.2018.01.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165188918300174
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jedc.2018.01.017?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. Abel Cadenillas & Fernando Zapatero, 2000. "Classical and Impulse Stochastic Control of the Exchange Rate Using Interest Rates and Reserves," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 141-156, April.
    2. Dominguez, Kathryn M & Frankel, Jeffrey A, 1993. "Does Foreign-Exchange Intervention Matter? The Portfolio Effect," American Economic Review, American Economic Association, vol. 83(5), pages 1356-1369, December.
    3. Zapatero, Fernando, 1995. "Equilibrium asset prices and exchange rates," Journal of Economic Dynamics and Control, Elsevier, vol. 19(4), pages 787-811, May.
    4. Ralf Korn, 1997. "Optimal Impulse Control When Control Actions Have Random Consequences," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 639-667, August.
    5. Cadenillas, Abel & Zapatero, Fernando, 1999. "Optimal Central Bank Intervention in the Foreign Exchange Market," Journal of Economic Theory, Elsevier, vol. 87(1), pages 218-242, July.
    6. Mundaca, Gabriela & Oksendal, Bernt, 1998. "Optimal stochastic intervention control with application to the exchange rate," Journal of Mathematical Economics, Elsevier, vol. 29(2), pages 225-243, March.
    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. Eyal Neuman & Alexander Schied & Chengguo Weng & Xiaole Xue, 2020. "A central bank strategy for defending a currency peg," Papers 2008.00470, arXiv.org.
    2. Eyal Neuman & Alexander Schied, 2022. "Protecting pegged currency markets from speculative investors," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 405-420, January.
    3. Cadenillas, Abel & Zapatero, Fernando, 1999. "Optimal Central Bank Intervention in the Foreign Exchange Market," Journal of Economic Theory, Elsevier, vol. 87(1), pages 218-242, July.
    4. Perera, Sandun & Gupta, Varun & Buckley, Winston, 2020. "Management of online server congestion using optimal demand throttling," European Journal of Operational Research, Elsevier, vol. 285(1), pages 324-342.
    5. Gregory Gagnon, 2019. "Vanishing central bank intervention in stochastic impulse control," Annals of Finance, Springer, vol. 15(1), pages 125-153, March.
    6. Sandun Perera & Winston Buckley, 2017. "On the existence and uniqueness of the optimal central bank intervention policy in a forex market with jumps," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(8), pages 877-885, August.
    7. Antonio Francisco A. Silva Jr., 2010. "Brazilian Strategy for Managing the Risk of Foreign Exchange Rate Exposure During a Crisis," Working Papers Series 207, Central Bank of Brazil, Research Department.
    8. Giorgio Ferrari & Tiziano Vargiolu, 2020. "On the singular control of exchange rates," Annals of Operations Research, Springer, vol. 292(2), pages 795-832, September.
    9. Yiannis Kamarianakis & Anastasios Xepapadeas, 2006. "Stochastic impulse control with discounted and ergodic optimization criteria: A comparative study for the control of risky holdings," Working Papers 0709, University of Crete, Department of Economics.
    10. Daniel Mitchell & Haolin Feng & Kumar Muthuraman, 2014. "Impulse Control of Interest Rates," Operations Research, INFORMS, vol. 62(3), pages 602-615, June.
    11. Jinbiao Wu, 2019. "Optimal exchange rates management using stochastic impulse control for geometric Lévy processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(2), pages 257-280, April.
    12. Lu Xiao & Huacong Ding & Yu Zhong & Chaojie Wang, 2023. "Optimal Control of Industrial Pollution under Stochastic Differential Models," Sustainability, MDPI, vol. 15(6), pages 1-16, March.
    13. Baccarin, Stefano, 2009. "Optimal impulse control for a multidimensional cash management system with generalized cost functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 198-206, July.
    14. Pasquariello, Paolo, 2010. "Central bank intervention and the intraday process of price formation in the currency markets," Journal of International Money and Finance, Elsevier, vol. 29(6), pages 1045-1061, October.
    15. Abel Cadenillas & Peter Lakner & Michael Pinedo, 2010. "Optimal Control of a Mean-Reverting Inventory," Operations Research, INFORMS, vol. 58(6), pages 1697-1710, December.
    16. Seydel, Roland C., 2009. "Existence and uniqueness of viscosity solutions for QVI associated with impulse control of jump-diffusions," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3719-3748, October.
    17. Stijn van Nieuwerburgh & Michael Kumhof, 2005. "Monetary Policy in an Equilibrium Portfolio Balance Model," 2005 Meeting Papers 851, Society for Economic Dynamics.
    18. Diego Zabaljauregui, 2019. "A fixed-point policy-iteration-type algorithm for symmetric nonzero-sum stochastic impulse control games," Papers 1909.03574, arXiv.org, revised Jun 2020.
    19. Christensen, Sören, 2014. "On the solution of general impulse control problems using superharmonic functions," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 709-729.
    20. Matteo Basei, 2019. "Optimal price management in retail energy markets: an impulse control problem with asymptotic estimates," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(3), pages 355-383, June.

    More about this item

    Keywords

    Exchange rate control; Partial information; Stochastic filtering; Impulse control; Quasi-variational inequalities;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • F31 - International Economics - - International Finance - - - Foreign Exchange
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets
    • E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies

    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:eee:dyncon:v:91:y:2018:i:c:p:369-390. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    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.