On the Dynamics of Semimartingales with Two Reflecting Barriers
(2013) In Journal of Applied Probability 50(3). p.671-685- Abstract
- We consider a semimartingale X which is reflected at an upper barrier T and a lower barrier S, where S and T are also semimartingales such that T is bounded away from S. First, we present an explicit construction of the reflected process. Then we derive a relationship in terms of stochastic integrals linking the reflected process and the local times at the respective bathers to X, S, and T. This result reveals the fundamental structural properties of the reflection mechanism. We also present a few results showing how the general relationship simplifies under additional assumptions on X, S, and T, e.g. if we take X, S, and T to be independent martingales (which satisfy some extra technical conditions).
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4172578
- author
- Pihlsgård, Mats LU and Glynn, Peter W.
- organization
- publishing date
- 2013
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Skorokhod problem, reflection, semimartingale, Levy process, martingale, stochastic integration
- in
- Journal of Applied Probability
- volume
- 50
- issue
- 3
- pages
- 671 - 685
- publisher
- Applied Probability Trust
- external identifiers
-
- wos:000325057600006
- scopus:84885105703
- ISSN
- 1475-6072
- language
- English
- LU publication?
- yes
- id
- 7383b495-157b-4afb-be99-9a95d49d50d8 (old id 4172578)
- date added to LUP
- 2016-04-01 10:23:13
- date last changed
- 2022-04-04 17:34:30
@article{7383b495-157b-4afb-be99-9a95d49d50d8, abstract = {{We consider a semimartingale X which is reflected at an upper barrier T and a lower barrier S, where S and T are also semimartingales such that T is bounded away from S. First, we present an explicit construction of the reflected process. Then we derive a relationship in terms of stochastic integrals linking the reflected process and the local times at the respective bathers to X, S, and T. This result reveals the fundamental structural properties of the reflection mechanism. We also present a few results showing how the general relationship simplifies under additional assumptions on X, S, and T, e.g. if we take X, S, and T to be independent martingales (which satisfy some extra technical conditions).}}, author = {{Pihlsgård, Mats and Glynn, Peter W.}}, issn = {{1475-6072}}, keywords = {{Skorokhod problem; reflection; semimartingale; Levy process; martingale; stochastic integration}}, language = {{eng}}, number = {{3}}, pages = {{671--685}}, publisher = {{Applied Probability Trust}}, series = {{Journal of Applied Probability}}, title = {{On the Dynamics of Semimartingales with Two Reflecting Barriers}}, volume = {{50}}, year = {{2013}}, }