Related papers: Information-Based Martingale Optimal Transport
The marginal maximum a posteriori probability (MAP) estimation problem, which calculates the mode of the marginal posterior distribution of a subset of variables with the remaining variables marginalized, is an important inference problem…
In this paper we consider a method of solving optimal stopping problems in discrete and continuous time based on their dual representation. A novel and generic simulation-based optimization algorithm not involving nested simulations is…
While optimal transport (OT) enforces a rigid constraint by requiring two measures to be matched exactly, partial optimal transport relaxes this requirement by allowing mass to remain unmatched through a global budget, scalar rebate, or…
Optimal Transport (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate the…
We consider the problem of solving TAP mean field equations by iteration for Ising model with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical…
The basic problem of optimal transportation consists in minimizing the expected costs $\mathbb {E}[c(X_1,X_2)]$ by varying the joint distribution $(X_1,X_2)$ where the marginal distributions of the random variables $X_1$ and $X_2$ are…
Generative models for sequential data often struggle with sparsely sampled and high-dimensional trajectories, typically reducing the learning of dynamics to pairwise transitions. We propose Interpolative Multi-Marginal Flow Matching…
In this article we study and classify optimal martingales in the dual formulation of optimal stopping problems. In this respect we distinguish between weakly optimal and surely optimal martingales. It is shown that the family of weakly…
In this article we discuss the problem of calculating optimal model-independent (robust) bounds for the price of Asian options with discrete and continuous averaging. We will give geometric characterisations of the maximising and the…
System optimum (SO) routing, wherein the total travel time of all users is minimized, is a holy grail for transportation authorities. However, SO routing may discriminate against users who incur much larger travel times than others to…
In the stochastic knapsack problem, we are given a knapsack of size B, and a set of jobs whose sizes and rewards are drawn from a known probability distribution. However, we know the actual size and reward only when the job completes. How…
We develop a numerical method for the martingale analogue of the Benamou--Brenier optimal transport problem, which seeks a martingale interpolating two prescribed marginals which is closest to the Brownian motion. Recent contributions have…
We establish dual attainment for the multimarginal, multi-asset martingale optimal transport (MOT) problem, a fundamental question in the mathematical theory of model-independent pricing and hedging in quantitative finance. Our main result…
The multi-armed bandit (MAB) model is one of the most classical models to study decision-making in an uncertain environment. In this model, a player chooses one of $K$ possible arms of a bandit machine to play at each time step, where the…
We study the problem of estimating latent population flows from aggregated count data. This problem arises when individual trajectories are not available due to privacy issues or measurement fidelity. Instead, the aggregated observations…
The martingale part in the semimartingale decomposition of a Brownian motion with respect to an enlargement of its filtration, is an anticipative mapping of the given Brownian motion. In analogy to optimal transport theory, we define causal…
We explore the structure of solutions to a family of non-linear martingale optimal transport (MOT) problems that involve conditional expectations in the objective functional. En route general results concerning optimization over…
Molecular motors are in charge of almost every process in the life cycle of cells, such as protein synthesis, DNA replication, and cell locomotion, hence being of crucial importance for understanding the cellular dynamics. However, given…
In this work, the authors address the Optimal Transport (OT) problem on graphs using a proximal stabilized Interior Point Method (IPM). In particular, strongly leveraging on the induced primal-dual regularization, the authors propose to…
This paper proposes an optimal allocation problem with ramified transport technology in a spatial economy. Ramified transportation is used to model the transport economy of scale in group transportation observed widely in both nature and…