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References
- Bally, V. Approximation scheme for solutions of BSDE. Backward stochastic differential equations (Paris, 1995--1996), 177--191, Pitman Res. Notes Math. Ser., 364, Longman, Harlow, 1997. MR1752682
- Bally, Vlad; PagÃs, Gilles; Printems, Jacques. A quantization tree method for pricing and hedging multidimensional American options. Math. Finance 15 (2005), no. 1, 119--168. MR2116799 (2005k:91142)
- Bender, C. and Denk R. Forward Simulation of Backward SDEs, preprint
- Bouchard, Bruno; Touzi, Nizar. Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations. Stochastic Process. Appl. 111 (2004), no. 2, 175--206. MR2056536 (2005b:65007)
- Briand, Philippe; Delyon, Bernard; MÃmin, Jean. Donsker-type theorem for BSDEs. Electron. Comm. Probab. 6 (2001), 1--14 (electronic). MR1817885 (2002f:60111)
- Chevance, D. Numerical methods for backward stochastic differential equations. Numerical methods in finance, 232--244, Publ. Newton Inst., Cambridge Univ. Press, Cambridge, 1997. MR1470517 (98i:60051)
- Delarue, FranÃois. On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case. Stochastic Process. Appl. 99 (2002), no. 2, 209--286. MR1901154 (2003c:60108)
- Delarue F. and Menozzi S. A forward-backward stochastic algorithm for quasi-linear PDEs, Ann. Appl. Probab., to appear.
- Douglas, Jim, Jr.; Ma, Jin; Protter, Philip. Numerical methods for forward-backward stochastic differential equations. Ann. Appl. Probab. 6 (1996), no. 3, 940--968. MR1410123 (97k:60160)
- Gobet, Emmanuel; Lemor, Jean-Philippe; Warin, Xavier. A regression-based Monte Carlo method to solve backward stochastic differential equations. Ann. Appl. Probab. 15 (2005), no. 3, 2172--2202. MR2152657
- Ladyv zenskaja, O. A.; Solonnikov, V. A.; Uralcprime ceva, N. N. Linear and quasilinear equations of parabolic type. (Russian) Translated from the Russian by S. Smith. Translations of Mathematical Monographs, Vol. 23 American Mathematical Society, Providence, R.I. 1967 xi+648 pp. MR0241822 (39 #3159b)
- Ma, Jin; Protter, Philip; San MartÃn, Jaime; Torres, Soledad. Numerical method for backward stochastic differential equations. Ann. Appl. Probab. 12 (2002), no. 1, 302--316. MR1890066 (2003d:60126)
- Ma, Jin; Protter, Philip; Yong, Jiong Min. Solving forward-backward stochastic differential equations explicitly---a four step scheme. Probab. Theory Related Fields 98 (1994), no. 3, 339--359. MR1262970 (94m:60118)
- Makarov, R. N. Numerical solution of quasilinear parabolic equations and backward stochastic differential equations. Russian J. Numer. Anal. Math. Modelling 18 (2003), no. 5, 397--412. MR2017290 (2004k:65017)
- M'{e}min J., Peng S., and Xu M. Convergence of solutions of discrete reflected BSDEs and simulations, preprint.
- Milstein, G. N.; Tretyakov, M. V.. Numerical algorithms for semilinear parabolic equations with small parameter based on approximation of stochastic equations. Math. Comp. 69 (2000), no. 229, 237--267. MR1653966 (2000i:65160)
- Ma, Jin; Yong, Jiongmin. Forward-backward stochastic differential equations and their applications. Lecture Notes in Mathematics, 1702. Springer-Verlag, Berlin, 1999. xiv+270 pp. ISBN: 3-540-65960-9 MR1704232 (2000k:60118)
- Ma, J.; Yong, J.. Approximate solvability of forward-backward stochastic differential equations. Appl. Math. Optim. 45 (2002), no. 1, 1--22. MR1861463 (2002j:35330)
- Pardoux, â¦.; Peng, S. G.. Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14 (1990), no. 1, 55--61. MR1037747 (91e:60171)
- Pardoux, Etienne; Tang, Shanjian. Forward-backward stochastic differential equations and quasilinear parabolic PDEs. Probab. Theory Related Fields 114 (1999), no. 2, 123--150. MR1701517 (2000f:60088)
- Zhang, Jianfeng. A numerical scheme for BSDEs. Ann. Appl. Probab. 14 (2004), no. 1, 459--488. MR2023027 (2004j:65015)
- Zhang J. The well-posedness of FBSDEs, Discrete and Continuous Dynamical Systems (B), to appear
- Zhang J. The well-posedness of FBSDEs (II), Submitted
- Zhang, Yinnan; Zheng, Weian. Discretizing a backward stochastic differential equation. Int. J. Math. Math. Sci. 32 (2002), no. 2, 103--116. MR1937828 (2003i:60105)
- Zhou, Xun Yu. Stochastic near-optimal controls: necessary and sufficient conditions for near-optimality. SIAM J. Control Optim. 36 (1998), no. 3, 929--947 (electronic). MR1613885 (99d:49050)

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