IDEAS home Printed from https://ideas.repec.org/p/hum/wpaper/sfb649dp2006-074.html
   My bibliography  Save this paper

Multiple Disorder Problems for Wiener and Compound Poisson Processes With Exponential Jumps

Author

Listed:
  • Pavel Gapeev

Abstract

The multiple disorder problem consists of finding a sequence of stopping times which are as close as possible to the (unknown) times of "disorder" when the distribution of an observed process changes its probability characteristics. We present a formulation and solution of the multiple disorder problem for a Wiener and a compound Poisson process with exponential jumps. The method of proof is based on reducing the initial optimal switching problems to the corresponding coupled optimal stopping problems and solving the equivalent coupled free-boundary problems by means of the smooth- and continuous-fit conditions.

Suggested Citation

  • Pavel Gapeev, 2006. "Multiple Disorder Problems for Wiener and Compound Poisson Processes With Exponential Jumps," SFB 649 Discussion Papers SFB649DP2006-074, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2006-074
    as

    Download full text from publisher

    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-074.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Bruckner, Matthias & Schabert, Andreas, 2006. "Can money matter for interest rate policy?," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2823-2857, December.
    2. Benhabib, Jess & Schmitt-Grohe, Stephanie & Uribe, Martin, 2001. "The Perils of Taylor Rules," Journal of Economic Theory, Elsevier, pages 40-69.
    3. Carlstrom, Charles T. & Fuerst, Timothy S., 2001. "Timing and real indeterminacy in monetary models," Journal of Monetary Economics, Elsevier, vol. 47(2), pages 285-298, April.
    4. Stephanie Schmitt-Grohe & Jess Benhabib & Martin Uribe, 2001. "Monetary Policy and Multiple Equilibria," American Economic Review, American Economic Association, pages 167-186.
    5. Jess Benhabib & Stephanie Schmitt-Grohe & Martin Uribe, 2003. "Backward-looking interest-rate rules, interest-rate smoothing, and macroeconomic instability," Proceedings, Federal Reserve Bank of Cleveland, pages 1379-1423.
    6. Leeper, Eric M., 1991. "Equilibria under 'active' and 'passive' monetary and fiscal policies," Journal of Monetary Economics, Elsevier, vol. 27(1), pages 129-147, February.
    7. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, January.
    8. Schabert, Andreas & Stoltenberg, Christian, 2005. "Money Demand and Macroeconomic Stability Revisited," CEPR Discussion Papers 4974, C.E.P.R. Discussion Papers.
    9. Woodford, Michael, 1994. "Monetary Policy and Price Level Determinacy in a Cash-in-Advance Economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 345-380.
    10. Feenstra, Robert C., 1986. "Functional equivalence between liquidity costs and the utility of money," Journal of Monetary Economics, Elsevier, vol. 17(2), pages 271-291, March.
    11. Mats Persson & Torsten Persson & Lars E. O. Svensson, 2006. "Time Consistency of Fiscal and Monetary Policy: A Solution," Econometrica, Econometric Society, vol. 74(1), pages 193-212, January.
    12. Sims, Christopher A, 1994. "A Simple Model for Study of the Determination of the Price Level and the Interaction of Monetary and Fiscal Policy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 381-399.
    13. Dupor, Bill, 2001. "Investment and Interest Rate Policy," Journal of Economic Theory, Elsevier, vol. 98(1), pages 85-113, May.
    14. Kurozumi, Takushi, 2006. "Determinacy and expectational stability of equilibrium in a monetary sticky-price model with Taylor rule," Journal of Monetary Economics, Elsevier, vol. 53(4), pages 827-846, May.
    15. Obstfeld, Maurice & Rogoff, Kenneth, 1983. "Speculative Hyperinflations in Maximizing Models: Can We Rule Them Out?," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 675-687, August.
    16. McCallum, Bennett T & Nelson, Edward, 1999. "An Optimizing IS-LM Specification for Monetary Policy and Business Cycle Analysis," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 31(3), pages 296-316, August.
    17. Charles T. Carlstrom & Timothy S. Fuerst, 2003. "Money Growth Rules and Price Level Determinacy," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(2), pages 263-275, April.
    18. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    19. Sargent, Thomas J & Wallace, Neil, 1975. ""Rational" Expectations, the Optimal Monetary Instrument, and the Optimal Money Supply Rule," Journal of Political Economy, University of Chicago Press, vol. 83(2), pages 241-254, April.
    20. Calvo, Guillermo A., 1983. "Staggered prices in a utility-maximizing framework," Journal of Monetary Economics, Elsevier, vol. 12(3), pages 383-398, September.
    21. Matsuyama, Kiminori, 1991. "Endogenous Price Fluctuations in an Optimizing Model of a Monetary Economy," Econometrica, Econometric Society, vol. 59(6), pages 1617-1631, November.
    22. Carlstrom, Charles T. & Fuerst, Timothy S., 2005. "Investment and interest rate policy: a discrete time analysis," Journal of Economic Theory, Elsevier, pages 4-20.
    23. Brock, William A, 1974. "Money and Growth: The Case of Long Run Perfect Foresight," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(3), pages 750-777, October.
    24. Jean-Pascal Benassy, 2000. "Price Level Determinacy under a Pure Interest Rate Peg," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(1), pages 194-211, January.
    25. Svensson, Lars E O, 1985. "Money and Asset Prices in a Cash-in-Advance Economy," Journal of Political Economy, University of Chicago Press, vol. 93(5), pages 919-944, October.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Multiple disorder problem; Wiener process; compound Poisson process; optimal switching; coupled optimal stopping problem; (integro-differential) coupled free-boundary problem; smooth and continuous fit; Ito-Tanaka-Meyer formula.;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hum:wpaper:sfb649dp2006-074. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (RDC-Team). General contact details of provider: http://edirc.repec.org/data/sohubde.html .

    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.

    We have no references for this item. You can help adding them by using 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.