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arXiv · 1802.08337

The left-curtain martingale coupling in the presence of atoms

David G. Hobson·Dominykas Norgilas
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Abstract

Beiglb\"ock and Juillet ("On a problem of optimal transport under marginal martingale constraints") introduced the left-curtain martingale coupling of probability measures $\mu$ and $\nu$, and proved that, when the initial law $\mu$ is continuous, it is supported by the graphs of two functions. We extend the later result by constructing the generalised left-curtain martingale coupling and show that for an arbitrary starting law $\mu$ it is characterised by two appropriately defined lower and upper functions. As an application of this result we derive the model-independent upper bound of an American put option. This extends recent results of Hobson and Norgilas ("Robust bounds for the American Put") on the atom-free case.

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David G. Hobson, Dominykas Norgilas. 2018-02-22. The left-curtain martingale coupling in the presence of atoms. https://arxiv.org/abs/1802.08337

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