A note on the planar Skorokhod embedding problem

Maher Boudabra

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arXiv · 2512.18353

A note on the planar Skorokhod embedding problem

Maher Boudabra

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Abstract

The planar Skorokhod embedding problem was first proposed and solved by R. Gross in 2019 [#gross2019]. Gross worked with probability distributions having finite second moment. In [#boudabra2019remarks, #Boudabra2020], the solutions extended to all distributions with a finite $p^{th}$ moment for $p>1$. The case $p=1$ remained uncovered since then. In this note we show that the planar Skorokhod embedding problem is solvable for $p=1$ when the Hilbert transform of its quantile function is integrable, effectively closing this line of investigation.

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Maher Boudabra. 2025-12-20. A note on the planar Skorokhod embedding problem. https://arxiv.org/abs/2512.18353

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