Section: New Results

Optimal transport

Participants : Aurélien Alfonsi, Benjamin Jourdain.

With J. Corbetta (postdoc financed by the chair financial risks), A. Alfonsi and B. Jourdain are interested in the time derivative of the Wasserstein distance between the marginals of two Markov processes. The Kantorovich duality leads to a natural candidate for this derivative. Up to the sign, it is the sum of the integrals with respect to each of the two marginals of the corresponding generator applied to the corresponding Kantorovich potential. For pure jump processes with bounded intensity of jumps, J. Corbetta, A. Alfonsi and B. Jourdain proved that the evolution of the Wasserstein distance is actually given by this candidate. In dimension one, they show that this remains true for Piecewise Deterministic Markov Processes [45].