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Impulse Control Method and Exchange Rate

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  • Monique Jeanblanc‐Picqué

Abstract

We control a diffusion process with constant coefficients in order to keep this process in a given band with impulse control methods. We prove that there exists an optimal control if the cost associated with each control is a fixed cost plus a proportional cost. We study the problem of the exchange rate and prove that it is possible to keep the exchange rate in a target zone with discrete interventions.

Suggested Citation

  • Monique Jeanblanc‐Picqué, 1993. "Impulse Control Method and Exchange Rate," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 161-177, April.
    • Handle: RePEc:bla:mathfi:v:3:y:1993:i:2:p:161-177
    DOI: 10.1111/j.1467-9965.1993.tb00085.x
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    Cited by:

    1. 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.
    2. Kazutoshi Yamazaki, 2016. "Optimality of two-parameter strategies in stochastic control," Papers 1605.04995, arXiv.org.
    3. Eyal Neuman & Alexander Schied & Chengguo Weng & Xiaole Xue, 2020. "A central bank strategy for defending a currency peg," Papers 2008.00470, arXiv.org.
    4. 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.
    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. Ohnishi, Masamitsu & Tsujimura, Motoh, 2006. "An impulse control of a geometric Brownian motion with quadratic costs," European Journal of Operational Research, Elsevier, vol. 168(2), pages 311-321, January.
    7. Diego Zabaljauregui, 2020. "Optimal market making under partial information and numerical methods for impulse control games with applications," Papers 2009.06521, arXiv.org.
    8. Milind M. Shrikhande, 1997. "The cost of doing business abroad and international capital market equilibrium," FRB Atlanta Working Paper 97-3, Federal Reserve Bank of Atlanta.
    9. Matteo Basei, 2018. "Optimal price management in retail energy markets: an impulse control problem with asymptotic estimates," Papers 1803.08166, arXiv.org, revised Mar 2019.
    10. 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.
    11. Giorgio Ferrari & Tiziano Vargiolu, 2020. "On the singular control of exchange rates," Annals of Operations Research, Springer, vol. 292(2), pages 795-832, September.

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