Bridging Schrödinger and Bass: A Semimartingale Optimal Transport Problem with Diffusion Control
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911734079422464 |
|---|---|
| author | Henry-Labordere, Pierre Loeper, Grégoire Mazhar, Othmane Pham, Huyên Touzi, Nizar |
| author_facet | Henry-Labordere, Pierre Loeper, Grégoire Mazhar, Othmane Pham, Huyên Touzi, Nizar |
| contents | We study a semimartingale optimal transport problem interpolating between the Schrödinger bridge and the stretched Brownian motion associated with the Bass solution of the Skorokhod embedding problem. The cost combines an entropy term on the drift with a quadratic penalization of the diffusion coefficient, leading to a stochastic control problem over drift and volatility. We establish a complete duality theory for this problem, despite the lack of coercivity in the diffusion component. In particular, we prove strong duality and dual attainment, and derive an equivalent reduced dual formulation in terms of a variational problem over terminal potentials. Optimal solutions are characterized by a coupled Schrödinger-Bass bridge system, involving a backward heat potential and a transport map given by the gradient of a $β$-convex function. This system interpolates between the classical Schrödinger system and the Bass martingale transport. Our results furnish a unified framework encompassing entropic and martingale optimal transport, and yield a variational foundation for data-driven diffusion models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27712 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bridging Schrödinger and Bass: A Semimartingale Optimal Transport Problem with Diffusion Control Henry-Labordere, Pierre Loeper, Grégoire Mazhar, Othmane Pham, Huyên Touzi, Nizar Probability Optimization and Control We study a semimartingale optimal transport problem interpolating between the Schrödinger bridge and the stretched Brownian motion associated with the Bass solution of the Skorokhod embedding problem. The cost combines an entropy term on the drift with a quadratic penalization of the diffusion coefficient, leading to a stochastic control problem over drift and volatility. We establish a complete duality theory for this problem, despite the lack of coercivity in the diffusion component. In particular, we prove strong duality and dual attainment, and derive an equivalent reduced dual formulation in terms of a variational problem over terminal potentials. Optimal solutions are characterized by a coupled Schrödinger-Bass bridge system, involving a backward heat potential and a transport map given by the gradient of a $β$-convex function. This system interpolates between the classical Schrödinger system and the Bass martingale transport. Our results furnish a unified framework encompassing entropic and martingale optimal transport, and yield a variational foundation for data-driven diffusion models. |
| title | Bridging Schrödinger and Bass: A Semimartingale Optimal Transport Problem with Diffusion Control |
| topic | Probability Optimization and Control |
| url | https://arxiv.org/abs/2603.27712 |