Stochastic optimal transport

The workshop studies stochastic extensions of optimal transport around three themes. Adapted or causal transport builds the flow of information over time into couplings, giving a natural framework for robust stochastic optimisation and mathematical finance. Semimartingale and martingale optimal transport couple continuous-time processes under constraints on drift and diffusion, with links to model-independent pricing and hedging. Diffusion-based geometries on spaces of probability measures generalise Wasserstein theory through the generator of a diffusion, producing new gradient-flow structures and functional inequalities. Specialists in transport, stochastic analysis, stochastic control and mathematical finance meet to identify shared structures.