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

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  • 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
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    References listed on IDEAS

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    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. Zapatero, Fernando, 1995. "Equilibrium asset prices and exchange rates," Journal of Economic Dynamics and Control, Elsevier, vol. 19(4), pages 787-811, May.
    3. 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.
    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)

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    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

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