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arXiv · 2208.02581

A mass transport approach to the optimization of adapted couplings of real valued random variables

Rémi Lassalle
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Abstract

In this work, we investigate an optimization problem over adapted couplings between pairs of real valued random variables, possibly describing random times. We relate those couplings to a specific class of causal transport plans between probabilities on the set of real numbers endowed with a filtration, for which their provide a specific representation, which is motivated by a precise characterization of the corresponding deterministic transport plans. From this, under mild hypothesis, the existence of a solution to the problem investigated here is obtained. Furthermore, several examples are provided, within this explicit framework.

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Rémi Lassalle. 2022-08-04. A mass transport approach to the optimization of adapted couplings of real valued random variables. https://arxiv.org/abs/2208.02581

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