Related papers: Relaxed multi-marginal costs and quantization effe…
This paper studies probabilistic dual frames and the associated dual frame potentials from the perspective of optimal mass transport. The main contribution of this work shows that given a probabilistic frame, its associated dual frame…
We establish weak limits for the empirical entropy regularized optimal transport cost, the expectation of the empirical plan and the conditional expectation. Our results require only uniform boundedness of the cost function and no…
Consider a transportation problem with sets of sources and sinks. There are profits and prices on the edges. The goal is to maximize the profit while meeting the following constraints; the total flow going out of a source must not exceed…
We consider the strictly correlated electron (SCE) limit of the fermionic quantum many-body problem in the second-quantized formalism. This limit gives rise to a multi-marginal optimal transport (MMOT) problem. Here the marginal state space…
We consider the martingale optimal transport duality for c\`adl\`ag processes with given initial and terminal laws. Strong duality and existence of dual optimizers (robust semi-static superhedging strategies) are proved for a class of…
We consider an optimal transportation problem with more than two marginals. We use a family of semi-Riemannian metrics derived from the mixed, second order partial derivatives of the cost function to provide upper bounds for the dimension…
A general framework is given to analyze the falsifiability of economic models based on a sample of their observable components. It is shown that, when the restrictions implied by the economic theory are insufficient to identify the unknown…
This paper proves the existence of optimal stopping times via elementary functional analytic arguments. The problem is first relaxed into a convex optimization problem over a closed convex subset of the unit ball of the dual of a Banach…
We combine the fields of heuristic optimization and optimal stopping. We propose a strategy for benchmarking randomized optimization algorithms that minimizes the expected total cost for obtaining a good solution with an optimal number of…
Finding the global minimum of a cost function given by the sum of a quadratic and a linear form in N real variables over (N-1)- dimensional sphere is one of the simplest, yet paradigmatic problems in Optimization Theory known as the "trust…
We consider the problem of optimal transportation with quadratic cost between a empirical measure and a general target probability on R d , with d $\ge$ 1. We provide new results on the uniqueness and stability of the associated optimal…
In this paper we derive robust super- and subhedging dualities for contingent claims that can depend on several underlying assets. In addition to strict super- and subhedging, we also consider relaxed versions which, instead of eliminating…
We study stability and sample complexity properties of divergence regularized optimal transport (DOT). First, we obtain quantitative stability results for optimizers of DOT measured in Wasserstein distance, which are applicable to a wide…
We analyze continuous optimal transport problems in the so-called Kantorovich form, where we seek a transport plan between two marginals that are probability measures on compact subsets of Euclidean space. We consider the case of…
The paper studies a general norm minimization problem on a product of normed vector spaces. We establish dual necessary and sufficient optimality conditions and derive explicit formulas for the corresponding solution sets. These formulas…
We introduce an efficient computational framework for solving a class of multi-marginal martingale optimal transport problems, which includes many robust pricing problems of large financial interest. Such problems are typically…
We study the semi-discrete formulation of one-dimensional partial optimal transport with quadratic cost, where a probability density is partially transported to a finite sum of Dirac masses of smaller total mass. This problem arises…
We analyze controlled mass transportation plans with free end-time that minimize the transport cost induced by the generating function of a Lagrangian within a bounded domain, in addition to costs incurred as export and import tariffs at…
In this work we study a special minimax problem where there are linear constraints that couple both the minimization and maximization decision variables. The problem is a generalization of the traditional saddle point problem (which does…
We are concerned with the relaxation and existence theories of a general class of geometrical minimisation problems, with action integrals defined via differential forms over fibre bundles. We find natural algebraic and analytic conditions…