Non-conservative optimal transport
Portfolio Management
2025-10-07 v1 Optimization and Control
Probability
Abstract
Motivated by optimal re-balancing of a portfolio, we formalize an optimal transport problem in which the transported mass is scaled by a mass-change factor depending on the source and destination. This allows direct modeling of the creation or destruction of mass. We discuss applications and position the framework alongside unbalanced, entropic, and unnormalized optimal transport. The existence of optimal transport plans and strong duality are established. The existence of optimal maps are deduced in two central regimes, i.e., perturbative mass-change and quadratic mass-loss. For costs we derive the analogue of the Benamou-Brenier dynamic formulation.
Cite
@article{arxiv.2510.03332,
title = {Non-conservative optimal transport},
author = {Gabriela Kováčová and Georg Menz and Niket Patel},
journal= {arXiv preprint arXiv:2510.03332},
year = {2025}
}