27 research outputs found
Time discretization and Markovian iteration for coupled FBSDEs
In this paper we lay the foundation for a numerical algorithm to simulate
high-dimensional coupled FBSDEs under weak coupling or monotonicity conditions.
In particular, we prove convergence of a time discretization and a Markovian
iteration. The iteration differs from standard Picard iterations for FBSDEs in
that the dimension of the underlying Markovian process does not increase with
the number of iterations. This feature seems to be indispensable for an
efficient iterative scheme from a numerical point of view. We finally suggest a
fully explicit numerical algorithm and present some numerical examples with up
to 10-dimensional state space.Comment: Published in at http://dx.doi.org/10.1214/07-AAP448 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A parallel four step domain decomposition scheme for coupled forward–backward stochastic differential equations
AbstractMotivated by the idea of imposing paralleling computing on solving stochastic differential equations (SDEs), we introduce a new domain decomposition scheme to solve forward–backward stochastic differential equations (FBSDEs) parallel. We reconstruct the four step scheme in Ma et al. (1994) [1] and then associate it with the idea of domain decomposition methods. We also introduce a new technique to prove the convergence of domain decomposition methods for systems of quasilinear parabolic equations and use it to prove the convergence of our scheme for the FBSDEs