Sampling of probability measures in the convex order by Wasserstein projection

DOI10.1214/19-AIHP1014zbMath1469.60065arXiv1709.05287OpenAlexW2916196187MaRDI QIDQ2227463

Aurélien Alfonsi, Jacopo Corbetta, Benjamin Jourdain

Publication date: 15 February 2021

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.05287

zbMATH Keywords

linear programmingWasserstein distanceconvex ordermartingale optimal transportsampling techniques

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) (90C08) Variational problems in a geometric measure-theoretic setting (49Q20) Derivative securities (option pricing, hedging, etc.) (91G20)

Related Items (18)

Instability of martingale optimal transport in dimension \(\mathrm{d}\ge 2\) ⋮ Martingale Wasserstein inequality for probability measures in the convex order ⋮ Approximation of martingale couplings on the line in the adapted weak topology ⋮ Monotone convex order for the McKean-Vlasov processes ⋮ Weak transport for non‐convex costs and model‐independence in a fixed‐income market ⋮ Weak Optimal Transport with Unnormalized Kernels ⋮ Lipschitz continuity of the Wasserstein projections in the convex order on the line ⋮ Continuity of the martingale optimal transport problem on the real line ⋮ Quantization and martingale couplings ⋮ Functional convex order for the scaled McKean-Vlasov processes ⋮ An optimal transport-based characterization of convex order ⋮ Backward and forward Wasserstein projections in stochastic order ⋮ Squared quadratic Wasserstein distance: optimal couplings and Lions differentiability ⋮ A new family of one dimensional martingale couplings ⋮ Optimal dual quantizers of \(1 D\log \)-concave distributions: uniqueness and Lloyd like algorithm ⋮ Shadow couplings ⋮ Convex order, quantization and monotone approximations of ARCH models ⋮ Stability of martingale optimal transport and weak optimal transport

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a problem of optimal transport under marginal martingale constraints
• An explicit martingale version of the one-dimensional Brenier theorem
• Model-independent bounds for option prices -- a mass transport approach
• On the rate of convergence in Wasserstein distance of the empirical measure
• Stability of the shadow projection and the left-curtain coupling
• Characterization of a class of weak transport-entropy inequalities on the line
• Stochastic and convex orders and lattices of probability measures, with a martingale interpretation
• Computational methods for martingale optimal transport problems
• Existence, duality, and cyclical monotonicity for weak transport costs
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• Kantorovich duality for general transport costs and applications
• A User's Guide to Measure Theoretic Probability
• Intrinsic Stationarity for Vector Quantization: Foundation of Dual Quantization
• Optimal quadratic quantization for numerics: the Gaussian case
• On a mixture of Brenier and Strassen Theorems
• A new class of costs for optimal transport planning
• Iterative Bregman Projections for Regularized Transportation Problems
• SAMPLING OF ONE-DIMENSIONAL PROBABILITY MEASURES IN THE CONVEX ORDER AND COMPUTATION OF ROBUST OPTION PRICE BOUNDS
• Stochastic Order Relations and Lattices of Probability Measures
• The Existence of Probability Measures with Given Marginals
• Generalized Iterative Scaling for Log-Linear Models

This page was built for publication: Sampling of probability measures in the convex order by Wasserstein projection