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Minimal Root’s embeddings for general starting and target distributions

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  • Wang, Jiajie

Abstract

Most results regarding Skorokhod embedding problems SEP so far rely on the assumption that the corresponding stopped process is uniformly integrable, which is equivalent to the convex ordering condition Uμ≤Uν when the underlying process is a local martingale. In this paper, we study the existence, construction of Root’s solutions to SEP, in the absence of this convex ordering condition. We replace the uniform integrability condition by the minimality condition (Monroe, 1972), as the criterion of “good” solutions. A sufficient and necessary condition (in terms of local time) for minimality is given. We also discuss the optimality of such minimal solutions. These results extend the generality of the results given by Cox and Wang (2013) and Gassiat et al. (2015). At last, we extend all the results above to multi-marginal embedding problems based on the work of Cox et al. (2018).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:2:p:521-544
    DOI: 10.1016/j.spa.2019.01.009
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    References listed on IDEAS

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    1. Gassiat, Paul & Oberhauser, Harald & dos Reis, Gonçalo, 2015. "Root’s barrier, viscosity solutions of obstacle problems and reflected FBSDEs," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4601-4631.
    2. 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.
    3. Pedersen, J. L. & Peskir, G., 2001. "The Azéma-Yor embedding in non-singular diffusions," Stochastic Processes and their Applications, Elsevier, vol. 96(2), pages 305-312, December.
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    Cited by:

    1. Erhan Bayraktar & Thomas Bernhardt, 2020. "On the Continuity of the Root Barrier," Papers 2010.14695, arXiv.org, revised Jul 2021.

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