Multilevel scheme for BSDEs

Plamen Turkedjiev (CMAP, École Polytechnique Paris)
Thursday, October 23, 2014 - 5:00pm
HU Berlin, Rudower Chaussee 25, 12489 Berlin, Room 1.115

We develop a multilevel approach to compute approximate solutions to backward dierential equations (BSDEs). The fully implementable algorithm of our multilevel scheme constructs sequential martingale control variates along a sequence of rening time-grids to reduce statistical approximation errors in an adaptive and generic way. We provide an error analysis with explicit and non-asymptotic error estimates for the multilevel scheme under general conditions on the forward process and the BSDE data. It is shown that the multilevel approach can reduce the computational complexity to achieve precision ?, ensured by error estimates, essentially by one order (in ?-1) in comparison to established methods, which is substantial. Computational examples support the validity of the theoretical analysis, demonstrating eciency improvements in practice.

This is a joint work with Dirk Becherer.