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Skew-Unfolding the Skorokhod Reflection of a Continuous Semimartingale

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Stochastic Analysis and Applications 2014

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 100))

Abstract

The Skorokhod reflection of a continuous semimartingale is unfolded, in a possibly skewed manner, into another continuous semimartingale on an enlarged probability space according to the excursion-theoretic methodology of [14]. This is done in terms of a skew version of the Tanaka equation, whose properties are studied in some detail. The result is used to construct a system of two diffusive particles with rank-based characteristics and skew-elastic collisions. Unfoldings of conventional reflections are also discussed, as are examples involving skew Brownian Motions and skew Bessel processes.

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Acknowledgments

We are indebted to Marcel Nutz and Daniel Ocone for stimulating discussions, to Vilmos Prokaj and Johannes Ruf for their careful reading of the manuscript and for their suggestions, and to the referee for simplifying the last part of our argument in Example 2. We dedicate this paper to Terry Lyons on the occasion of his 60th birthday.

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Authors and Affiliations

  1. Department of Statistics and Applied Probability, University of California, South Hall, Santa Barbara, CA, 93106, USA

    Tomoyuki Ichiba

  2. Department of Mathematics, Columbia University, New York, NY, USA

    Ioannis Karatzas

  3. INTECH Investment Management, One Palmer Square, Suite 441, Princeton, NJ, 08542, USA

    Ioannis Karatzas

Authors
  1. Tomoyuki Ichiba
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  2. Ioannis Karatzas
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Correspondence to Tomoyuki Ichiba .

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Editors and Affiliations

  1. Department of Mathematics, Imperial College, London, United Kingdom

    Dan Crisan

  2. Mathematical Institute, University of Oxford, Oxford, United Kingdom

    Ben Hambly

  3. Department of Mathematics and IROM, University of Texas McCombs School of Business, Austin, Texas, USA

    Thaleia Zariphopoulou

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Ichiba, T., Karatzas, I. (2014). Skew-Unfolding the Skorokhod Reflection of a Continuous Semimartingale. In: Crisan, D., Hambly, B., Zariphopoulou, T. (eds) Stochastic Analysis and Applications 2014. Springer Proceedings in Mathematics & Statistics, vol 100. Springer, Cham. https://doi.org/10.1007/978-3-319-11292-3_13

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