Journal
ANNALS OF APPLIED PROBABILITY
Volume 14, Issue 1, Pages 459-488Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/aoap/1075828058
Keywords
backward SDEs; L-infinity-Lipschitz functionals; step processes; L-2-regularity
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In this paper we propose a numerical scheme for a class of backward stochastic differential equations (BSDEs) with possible path-dependent terminal values. We prove that our scheme converges in the strong L-2 sense and derive its rate of convergence. As an intermediate step we prove an L-2-type regularity of the solution to such BSDEs. Such a notion of regularity, which can be thought of as the modulus of continuity of the paths in an L-2 sense, is new. Some other features of our scheme include the following: (i) both components of the solution are approximated by step processes (i.e., piecewise constant processes); (ii) the regularity requirements on the coefficients are practically minimum; (iii) the dimension of the integrals involved in the approximation is independent of the partition size.
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