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Non-conservative optimal transport

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  • Gabriela Kov'av{c}ov'a
  • Georg Menz
  • Niket Patel

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 $\ell_p$ costs we derive the analogue of the Benamou-Brenier dynamic formulation.

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  • Gabriela Kov'av{c}ov'a & Georg Menz & Niket Patel, 2025. "Non-conservative optimal transport," Papers 2510.03332, arXiv.org.
    • Handle: RePEc:arx:papers:2510.03332
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    References listed on IDEAS

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    1. Andrew J. Morton & Stanley R. Pliska, 1995. "Optimal Portfolio Management With Fixed Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 5(4), pages 337-356, October.
    2. Yuri Kabanov, 2009. "Markets with Transaction Costs. Mathematical Theory," Post-Print hal-00488168, HAL.
    3. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
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