IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v96y2015icp262-268.html
   My bibliography  Save this article

Large deviations for the boundary local time of doubly reflected Brownian motion

Author

Listed:
  • Forde, Martin
  • Kumar, Rohini
  • Zhang, Hongzhong

Abstract

We compute a closed-form expression for the moment generating function fˆ(x;λ,α)=1λEx(eαLτ), where Lt is the local time at zero for standard Brownian motion with reflecting barriers at 0 and b, and τ∼Exp(λ) is independent of W. By analyzing how and where fˆ(x;⋅,α) blows up in λ, a large-time large deviation principle (LDP) for Lt/t is established using a Tauberian result and the Gärtner–Ellis Theorem.

Suggested Citation

  • Forde, Martin & Kumar, Rohini & Zhang, Hongzhong, 2015. "Large deviations for the boundary local time of doubly reflected Brownian motion," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 262-268.
    • Handle: RePEc:eee:stapro:v:96:y:2015:i:c:p:262-268
    DOI: 10.1016/j.spl.2014.09.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715214003150
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2014.09.004?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. de Jong, F, 1994. "A Univariate Analysis of EMS Exchange Rates Using a Target Zone Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 9(1), pages 31-45, Jan.-Marc.
    2. Svensson, Lars E. O., 1991. "The term structure of interest rate differentials in a target zone : Theory and Swedish data," Journal of Monetary Economics, Elsevier, vol. 28(1), pages 87-116, August.
    3. Stefan Gerhold & Paolo Guasoni & Johannes Muhle-Karbe & Walter Schachermayer, 2014. "Transaction costs, trading volume, and the liquidity premium," Finance and Stochastics, Springer, vol. 18(1), pages 1-37, January.
    4. Viatcheslav Gorovoi & Vadim Linetsky, 2004. "Black's Model of Interest Rates as Options, Eigenfunction Expansions and Japanese Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 49-78, January.
    5. Hanson, Steven D. & Myers, Robert J. & Hilker, James H., 1999. "Hedging With Futures And Options Under A Truncated Cash Price Distribution," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 31(3), pages 1-11, December.
    6. Paul R. Krugman, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(3), pages 669-682.
    7. Bertola, Giuseppe & Caballero, Ricardo J, 1992. "Target Zones and Realignments," American Economic Review, American Economic Association, vol. 82(3), pages 520-536, June.
    8. Hanson, Steven D. & Myers, Robert J. & Hilker, James H., 1999. "Hedging with Futures and Options under a Truncated Cash Price Distribution," Journal of Agricultural and Applied Economics, Cambridge University Press, vol. 31(3), pages 449-459, December.
    9. Clifford Ball & Antonio Roma, 1998. "Detecting mean reversion within reflecting barriers: application to the European Exchange Rate Mechanism," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(1), pages 1-15.
    10. Heber Farnsworth & Richard Bass, 2003. "The Term Structure with Semi-credible Targeting," Journal of Finance, American Finance Association, vol. 58(2), pages 839-866, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. H. Dharma Kwon & Hongzhong Zhang, 2015. "Game of Singular Stochastic Control and Strategic Exit," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 869-887, October.

    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, 2022. "Protecting pegged currency markets from speculative investors," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 405-420, January.
    2. Eyal Neuman & Alexander Schied, 2018. "Protecting Pegged Currency Markets from Speculative Investors," Papers 1801.07784, arXiv.org, revised Feb 2021.
    3. Eyal Neuman & Alexander Schied, 2016. "Optimal portfolio liquidation in target zone models and catalytic superprocesses," Finance and Stochastics, Springer, vol. 20(2), pages 495-509, April.
    4. António Portugal Duarte & João Sousa Andrade & Adelaide Duarte, 2013. "Exchange Rate Target Zones: A Survey Of The Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 27(2), pages 247-268, April.
    5. Bekaert, Geert & Gray, Stephen F., 1998. "Target zones and exchange rates:: An empirical investigation," Journal of International Economics, Elsevier, vol. 45(1), pages 1-35, June.
    6. Jesús Rodríguez López & Hugo Rodríguez Mendizábal, 2007. "The Optimal Degree of Exchange Rate Flexibility: a Target Zone Approach," Review of International Economics, Wiley Blackwell, vol. 15(4), pages 803-822, September.
    7. Beetsma, Roel M. W. J., 1995. "EMS exchange rate bands: a Monte Carlo investigation of three target zone models," Journal of International Money and Finance, Elsevier, vol. 14(2), pages 311-328, April.
    8. Ning Cai & Xuewei Yang, 2021. "A Computational Approach to First Passage Problems of Reflected Hyperexponential Jump Diffusion Processes," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 216-229, January.
    9. Miller, J. Isaac, 2011. "Testing the bounds: Empirical behavior of target zone fundamentals," Economic Modelling, Elsevier, vol. 28(4), pages 1782-1792, July.
    10. Peter P. Carr & Zura Kakushadze, 2017. "FX options in target zones," Quantitative Finance, Taylor & Francis Journals, vol. 17(10), pages 1477-1486, October.
    11. Eyal Neuman & Alexander Schied, 2015. "Optimal Portfolio Liquidation in Target Zone Models and Catalytic Superprocesses," Papers 1504.06031, arXiv.org, revised Jul 2015.
    12. Ribeiro de Castro, Claudia, 1999. "Inside and Outside the Band Exchange Rate Fluctuations for Brazil," LIDAM Discussion Papers IRES 2000004, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    13. Miller, J. Isaac & Park, Joon Y., 2005. "How They Interact to Generate Persistency in Memory," Working Papers 2005-01, Rice University, Department of Economics.
    14. Jess Rodr?uez L?ez & Hugo Rodr?uez Mendiz?al, 2002. "On the Choice of an Exchange Rate Regime: Target Zones Revisited," UFAE and IAE Working Papers 518.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    15. Qingpei Zang & Lixin Zhang, 2019. "Asymptotic Behaviour of the Trajectory Fitting Estimator for Reflected Ornstein–Uhlenbeck Processes," Journal of Theoretical Probability, Springer, vol. 32(1), pages 183-201, March.
    16. Taylor, Mark P. & Iannizzotto, Matteo, 2001. "On the mean-reverting properties of target zone exchange rates: a cautionary note," Economics Letters, Elsevier, vol. 71(1), pages 117-129, April.
    17. Marie Bessec, 2000. "Mean-Reversion versus PPP Adjustment: The Two Regimes of Exchange Rate Dynamics Under the EMS, 1979-1998," Econometric Society World Congress 2000 Contributed Papers 1305, Econometric Society.
    18. Mundaca, Gabriela, 2003. "A Drift of the "Drift Adjustment Method"," Memorandum 16/2002, Oslo University, Department of Economics.
    19. Jean-Pierre Laffargue & Sanvi Avouyi-Dovi, 1992. "Anticipations stabilisatrices dans un système de serpent monétaire. Théorie et application au système monétaire européen," Revue Économique, Programme National Persée, vol. 43(6), pages 1107-1128.
    20. Lai, Ching-chong & Fang, Chung-rou & Chang, Juin-jen, 2008. "Volatility trade-offs in exchange rate target zones," International Review of Economics & Finance, Elsevier, vol. 17(3), pages 366-379.

    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:stapro:v:96:y:2015:i:c:p:262-268. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.