An explicit solution to the Skorokhod embedding problem for functionals of excursions of Markov processes
AbstractWe 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.Â Oblój, M.Â 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.Â Oblój, M.Â 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 117 (2007)
Issue (Month): 4 (April)
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Umut Cetin & Robert Jarrow & Philip Protter & Yildiray Yildirim, 2004.
"Modeling Credit Risk with Partial Information,"
- David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
- 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.
- Haydyn Brown & David Hobson & L. C. G. Rogers, 2001. "Robust Hedging of Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 11(3), pages 285-314.
- Nikeghbali, Ashkan, 2006. "A class of remarkable submartingales," Stochastic Processes and their Applications, Elsevier, vol. 116(6), pages 917-938, June.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If references are entirely missing, you can add them using this form.