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September 2013 On the dynamics of semimartingales with two reflecting barriers
Mats Pihlsgård, Peter W. Glynn
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J. Appl. Probab. 50(3): 671-685 (September 2013). DOI: 10.1239/jap/1378401229

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 barriers 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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Mats Pihlsgård. Peter W. Glynn. "On the dynamics of semimartingales with two reflecting barriers." J. Appl. Probab. 50 (3) 671 - 685, September 2013. https://doi.org/10.1239/jap/1378401229

Information

Published: September 2013
First available in Project Euclid: 5 September 2013

zbMATH: 1282.60047
MathSciNet: MR3102508
Digital Object Identifier: 10.1239/jap/1378401229

Subjects:
Primary: 60G44, 60G51, 60H05
Secondary: 60G17

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 3 • September 2013
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