34 citations · 146 across the 31 of their papers we have counts for
40 papers
An ODE characterisation of multi-marginal optimal transport with pairwise cost functions
Luca Nenna, Brendan Pass
The purpose of this paper is to introduce a new numerical method to solve multi-marginal optimal transport problems with pairwise interaction costs. The complexity of multi-margina…
Robust risk management via multi-marginal optimal transport
Hamza Ennaji, Quentin Mérigot, Luca Nenna +1
We study the problem of maximizing a spectral risk measure of a given output function which depends on several underlying variables, whose individual distributions are known but wh…
A note on Cournot-Nash equilibria and Optimal Transport between unequal dimensions
Luca Nenna, Brendan Pass
This note is devoted to study a class of games with a continuum of players for which Cournot-Nash equilibria can be obtained by minimisation of some cost related to Optimal Transpo…
Lorenz map, inequality ordering and curves based on multidimensional rearrangements
Yanqin Fan, Marc Henry, Brendan Pass +1
We propose a multivariate extension of the Lorenz curve based on multivariate rearrangements of optimal transport theory. We define a vector Lorenz map as the integral of the vecto…
Monge solutions and uniqueness in multi-marginal optimal transport: weaker conditions on the cost, stronger conditions on the marginals
Brendan Pass, Adolfo Vargas-Jiménez
We establish a general condition on the cost function to obtain uniqueness and Monge solutions in the multi-marginal optimal transport problem, under the assumption that a given co…
Transport type metrics on the space of probability measures involving singular base measures
Luca Nenna, Brendan Pass
We develop the theory of a metric, which we call the -based Wasserstein metric and denote by , on the set of probability measures on a domain $X \subseteq \…