A mass transport approach to the optimization of adapted couplings of real valued random variables
Probability
2022-10-18 v2 Optimization and Control
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.
Keywords
Cite
@article{arxiv.2208.02581,
title = {A mass transport approach to the optimization of adapted couplings of real valued random variables},
author = {Rémi Lassalle},
journal= {arXiv preprint arXiv:2208.02581},
year = {2022}
}
Comments
Document of work in progess