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On the Continuity of the Root Barrier

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  • Erhan Bayraktar
  • Thomas Bernhardt

Abstract

We show that the barrier function in Root's solution to the Skorokhod embedding problem is continuous and finite at every point where the target measure has no atom and its absolutely continuous part is locally bounded away from zero.

Suggested Citation

  • Erhan Bayraktar & Thomas Bernhardt, 2020. "On the Continuity of the Root Barrier," Papers 2010.14695, arXiv.org, revised Jul 2021.
    • Handle: RePEc:arx:papers:2010.14695
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    References listed on IDEAS

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    1. Alexander M. G. Cox & Jiajie Wang, 2011. "Root's barrier: Construction, optimality and applications to variance options," Papers 1104.3583, arXiv.org, revised Mar 2013.
    2. Peter Carr & Roger Lee, 2010. "Hedging variance options on continuous semimartingales," Finance and Stochastics, Springer, vol. 14(2), pages 179-207, April.
    3. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
    4. Mathias Beiglboeck & Alexander Cox & Martin Huesmann, 2017. "The geometry of multi-marginal Skorokhod Embedding," Papers 1705.09505, arXiv.org.
    5. Wang, Jiajie, 2020. "Minimal Root’s embeddings for general starting and target distributions," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 521-544.
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