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On the Dynamics of Semimartingales with Two Reflecting Barriers

Pihlsgård, Mats ; Glynn, Peter W.

Journal of applied probability, 2013-09, Vol.50 (3), p.671-685 [Periódico revisado por pares]

Cambridge, UK: Cambridge University Press

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Título:
On the Dynamics of Semimartingales with Two Reflecting Barriers
Autor: Pihlsgård, Mats ; Glynn, Peter W.
Assuntos: 60G17 ; 60G44 ; 60G51 ; 60H05 ; Barriers ; Cauchy Schwarz inequality ; Construction ; Dams ; Dynamics ; Integrals ; Integration by parts ; Joining ; Levy process ; Lévy process ; martingale ; Martingales ; Matematik ; Mathematical analysis ; Mathematical moments ; Mathematics ; Natural Sciences ; Naturvetenskap ; Probability distribution ; Probability Theory and Statistics ; Reflection ; Same sex marriage ; Sannolikhetsteori och statistik ; semimartingale ; Skorokhod problem ; stochastic integration ; Stochastic models ; Stochastic processes ; Stochasticity ; Studies
É parte de: Journal of applied probability, 2013-09, Vol.50 (3), p.671-685
Notas: ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
Descrição: 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).
Editor: Cambridge, UK: Cambridge University Press
Idioma: Inglês

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On the Dynamics of Semimartingales with Two Reflecting Barriers

Pihlsgård, Mats ; Glynn, Peter W.

Cambridge, UK: Cambridge University Press

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