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On the Dynamics of Semimartingales with Two Reflecting Barriers

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Author

Summary, in English

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).

Department/s

Publishing year

2013

Language

English

Pages

671-685

Publication/Series

Journal of Applied Probability

Volume

50

Issue

3

Document type

Journal article

Publisher

Applied Probability Trust

Topic

  • Probability Theory and Statistics

Keywords

  • Skorokhod problem
  • reflection
  • semimartingale
  • Levy process
  • martingale
  • stochastic integration

Status

Published

Research group

  • Geriatrics
  • Geriatric Medicine

ISBN/ISSN/Other

  • ISSN: 1475-6072