High order weak Monte Carlo methods from the Cubature on Wiener space point of view for solving SDE's

  The "Cubature on Wiener space" algorithm can be regarded as a general approach to high order weak approximations. Based on this observation we will derive many well known weak discretisation schemes and optimise the computational effort required for a given accuracy of the approximation. We show that cubature can also help to overcome some stability difficulties. The cubature on Wiener space algorithm is frequently combined with partial sampling techniques and we outline an extension to these methods to reduce the variance of the samples. We apply the extended method to examples arising in mathematical finance. Joint work of G. Gyurko, C. Litterer and T. Lyons