We introduce a forward scheme to simulate backward SDEs. Compared to existing schemes, we avoid high order nestings of conditional expectations backwards in time. In this way the error, when approximating the conditional expectation, in dependence of the time partition is significantly reduced. Besides this generic result, we present an implementable algorithm and provide an error analysis for it. Finally, we demonstrate the strength of the new algorithm by solving some financial problems numerically.

Arbitrage, Pricing, Quadratic variation, Robust hedging, G10, G13,

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

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