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Numerical algorithms for forward-backward stochastic differential equations. (English) Zbl 1114.60054
Summary: Efficient numerical algorithms are proposed for a class of forward-backward stochastic differential equations (FBSDEs) connected with semilinear parabolic partial differential equations. As in [{\it J. Douglas jun., J. Ma} and {\it P. Protter}, Ann. Appl. Probab. 6, No. 3, 940--968 (1996; Zbl 0861.65131)], the algorithms are based on the known four-step scheme for solving FBSDEs. The corresponding semilinear parabolic equation is solved by layer methods which are constructed by means of a probabilistic approach. The derivatives of the solution $u$ of the semilinear equation are found by finite differences. The forward equation is simulated by mean-square methods of order 1/2 and 1. Corresponding convergence theorems are proved. Along with the algorithms for FBSDEs on a fixed finite time interval, we also construct algorithms for FBSDEs with random terminal time. The results obtained are supported by numerical experiments.

60H35Computational methods for stochastic equations
65C30Stochastic differential and integral equations
60H10Stochastic ordinary differential equations
62P05Applications of statistics to actuarial sciences and financial mathematics
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