A unifying framework for economic equilibrium and optimal transport in infinite-dimensional Hilbert spaces
Under what conditions can economic equilibrium be represented as an optimal-transport problem in an infinite-dimensional Hilbert space?
- Status
- Public working paper · SSRN 4772016
- Role
- Sole author
- Authors
- Ian Helfrich
- Method
- optimal transport · tensor-valued measures · nonlinear operator theory
- What this record does not establish
- This record states the paper's question and approach; the theorem statements and their assumptions are in the SSRN manuscript.
Public artifactsPublic working paper
Abstract
Summary
A theoretical working paper connecting economic equilibrium and optimal transport when the economic object is a function or distribution rather than a finite vector.
Question
How does a mass distribution reallocate toward a new spatial target?
Choose the shape and location of a target distribution, then compute transport from the same fixed source.
The first number summarizes how far mass moves. The remaining figures separate movement of conditional means from residual spread and report solver accuracy.
Specialist diagnostics
Run transport to see the regularized W₂ approximation, iteration count, and marginal error.
The reported RMS includes both displacement of each conditional mean and the coupling's conditional variance. Source and target marginals must converge to the displayed numerical tolerance.
Methods and notes
This sole-authored 2024 working paper asks how economic equilibrium and optimal transport relate in infinite-dimensional Hilbert spaces.
BibTeX
Citation
@misc{helfrich2024unifying,
author = {Helfrich, Ian},
title = {A unifying framework for economic equilibrium and optimal transport in infinite-dimensional Hilbert spaces},
year = {2024},
note = {Working paper, SSRN 4772016},
url = {https://ssrn.com/abstract=4772016}
}