Unbiased Monte Carlo estimate of stochastic differential equations expectations

Mahamadou Doumbia, Nadia Oudjane,  Xavier Warin 

We propose an unbiased Monte Carlo method to compute E(g(XT ))  where g is a Lipschitz function and X an Ito process. This approach extends the method proposed in [16] to the case where X is solution of a multidimensional stochastic differential equation with varying drift and diffusion coefficients. A variance reduction method relying on interacting particle systems is also developed.

Key words: unbiased estimate, linear parabolic PDEs, interacting particle systems