"Pathwise optimal transport bounds between a one-dimensional diffusion and its Euler scheme"

Stochastic Analysis Seminar Series

(joint work with Aurélien Alfonsi and Arturo Kohatsu-Higa)

We are interested in the Wasserstein distance on the space of continuous sample-paths equipped with the supremum norm between the laws of a uniformly elliptic one-dimensional diffusion process and its continuous-time Euler scheme with N steps. This distance controls the discretization biais for a large class of path-dependent payoffs.

Its convergence rate to 0 is clearly intermediate between -the rate -1/2 of the strong error estimation obtained when coupling the stochastic differential equation and its Euler scheme with the same Brownian motion -and the rate -1 of the weak error estimation obtained when comparing the expectations of the same function of the diffusion and its Euler scheme at the terminal time.


For uniformly elliptic one-dimensional stochastic differential equations, we prove that this rate is not worse than -2/3.



Monday, October 14, 2013 - 15:45
to 16:45