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Classical and Impulse Stochastic Control of the Exchange Rate Using Interest Rates and Reserves

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  • Abel Cadenillas
  • Fernando Zapatero

Abstract

We consider the problem of a Central Bank that wants the exchange rate to be as close as possible to a given target, and in order to do that uses both the interest rate level and interventions in the foreign exchange market. We model this as a mixed classical-impulse stochastic control problem, and provide for the first time a solution to that kind of problem. We give examples of solutions that allow us to perform an interesting economic analysis of the optimal strategy of the Central Bank. Copyright Blackwell Publishers, Inc..

Suggested Citation

  • 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.
  • Handle: RePEc:bla:mathfi:v:10:y:2000:i:2:p:141-156
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    Citations

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    Cited by:

    1. Ibtissam Hdhiri & Monia Karouf, 2011. "Risk sensitive impulse control of non-Markovian processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(1), pages 1-20, August.
    2. repec:eee:apmaco:v:265:y:2015:i:c:p:163-175 is not listed on IDEAS
    3. repec:spr:compst:v:74:y:2011:i:1:p:1-20 is not listed on IDEAS
    4. Shangzhen Luo & Michael Taksar, 2011. "Minimal Cost of a Brownian Risk without Ruin," Papers 1112.4005, arXiv.org.
    5. 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.
    6. 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.
    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. 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.
    9. Andrew W. Lo & Harry Mamaysky & Jiang Wang, 2004. "Asset Prices and Trading Volume under Fixed Transactions Costs," Journal of Political Economy, University of Chicago Press, vol. 112(5), pages 1054-1090, October.
    10. Luo, Shangzhen & Taksar, Michael, 2012. "Minimal cost of a Brownian risk without ruin," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 685-693.
    11. 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.
    12. Jiatu Cai & Mathieu Rosenbaum & Peter Tankov, 2015. "Asymptotic Lower Bounds for Optimal Tracking: a Linear Programming Approach," Papers 1510.04295, arXiv.org.
    13. Giorgio Ferrari & Tiziano Vargiolu, 2017. "On the Singular Control of Exchange Rates," Papers 1712.02164, arXiv.org.
    14. Dmitry B. Rokhlin & Georgii Mironenko, 2016. "Regular finite fuel stochastic control problems with exit time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(1), pages 105-127, August.

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