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On the Dynamics of Semimartingales with Two Reflecting Barriers

Pihlsgård, Mats LU and Glynn, Peter W. (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).
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author
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organization
publishing date
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}},
}