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An explicit solution to the Skorokhod embedding problem for functionals of excursions of Markov processes

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  • Oblój, Jan

Abstract

We develop an explicit non-randomized solution to the Skorokhod embedding problem in an abstract setup of signed functionals of excursions of Markov processes. Our setting allows us to solve the Skorokhod embedding problem, in particular, for the age process of excursions of a Markov process, for diffusions and their signed age processes, for Azéma's martingale and for Bessel processes of dimension smaller than 2. This work is a continuation and an important generalization of Oblój and Yor [J. Oblój, M. Yor, An explicit Skorokhod embedding for the age of Brownian excursions and Azéma martingale, Stochastic Process. Appl. 110 (1) (2004) 83-110]. Our methodology is based on excursion theory and the solution to the Skorokhod embedding problem is described in terms of the Itô measure of the functional. We also derive an embedding for positive functionals and we correct a mistake in the formula of Oblój and Yor [J. Oblój, M. Yor, An explicit Skorokhod embedding for the age of Brownian excursions and Azéma martingale, Stochastic Process. Appl. 110 (1) (2004) 83-110] for measures with atoms.

Suggested Citation

  • Oblój, Jan, 2007. "An explicit solution to the Skorokhod embedding problem for functionals of excursions of Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 117(4), pages 409-431, April.
  • Handle: RePEc:eee:spapps:v:117:y:2007:i:4:p:409-431
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    1. Umut Çetin & Robert Jarrow & Philip Protter & Yildiray Yildirim, 2008. "Modeling Credit Risk With Partial Information," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 23, pages 579-590 World Scientific Publishing Co. Pte. Ltd..
    2. Vallois, P., 1992. "Quelques inégalités avec le temps local en zero du mouvement Brownien," Stochastic Processes and their Applications, Elsevier, vol. 41(1), pages 117-155, May.
    3. Nikeghbali, Ashkan, 2006. "A class of remarkable submartingales," Stochastic Processes and their Applications, Elsevier, vol. 116(6), pages 917-938, June.
    4. Haydyn Brown & David Hobson & L. C. G. Rogers, 2001. "Robust Hedging of Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 11(3), pages 285-314.
    5. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
    6. Oblój, Jan & Yor, Marc, 2004. "An explicit Skorokhod embedding for the age of Brownian excursions and Azéma martingale," Stochastic Processes and their Applications, Elsevier, vol. 110(1), pages 83-110, March.
    7. Cox, A. M. G. & Hobson, D. G., 2004. "An optimal Skorokhod embedding for diffusions," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 17-39, May.
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