Minimal Root’s embeddings for general starting and target distributions

Jiajie Wang

Stochastic Processes and their Applications, 2020, vol. 130, issue 2, 521-544

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).

Keywords: Minimal stopping time; Multi-marginal embedding problem; Obstacle problem; Root’s barrier; Skorokhod embedding; Viscosity solution (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2019.01.009

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