A numerical scheme for BSDEs

Nualart, D. (1995). <i>The Malliavin Calculus and Related Topics</i>. Springer, New York.

Bally, V. (1995). An approximation scheme for BSDEs and applications to control and nonlinear PDEs. Prepublication 95-15 du Laboratoire de Statistique et Processus de l'Universite du Maine.

Björk, T. (1998). <i>Arbitrage Theory in Continuous Time.</i> Oxford Univ. Press.

Chevance, D. (1996). Ph.D. thesis, Univ. Provence.

Dai, M. and Jiang, L. (2000). On path-dependent options. In <i>Mathematical Finance---Theory and Applications</i> (J. Yong and R. Cont, eds.) 290--316. Higher Education Press, China.

El Karoui, N. and Mazliak, L. (1997). <i>Backward Stochastic Differential Equations</i>. Longman, Harlow.

Gikhman, I. I. and Skorohod, A. V. (1972). <i>Stochastic Differential Equations</i>. Springer, New York.

Karatzas, I. and Shreve, S. E. (1987). <i>Brownian Motion and Stochastic Calculus</i>. Springer, New York.

Kloeden, P. E. and Platen, E. (1992). <i>Numerical Solution of Stochastic Differential Equations</i>. Springer, New York.

Zhang, J. (2001). Some fine properties of backward stochastic differential equations. Ph.D. dissertation, Purdue Univ.

Zhang, Y. and Zheng, W. (2001). Discretizing a backward stochastic differential equations. Preprint.

Asmussen, S., Glynn, P. and Pitman, J. (1995). Discretization error in simulation of one-dimensional reflecting Brownian motion. <i>Ann. Appl. Probab.</i> <b>5</b> 875--896.

Bismut, J. M. (1973). Théorie probabiliste du contrôle des diffusions. <i>Mem. Amer. Math. Soc.</i> <b>176</b>.

Briand, P., Delyon, B. and Mémin, J. (2001). Donsker-type theorem for BSDEs. <i>Electron. Comm. Probab.</i> <b>6</b> 1--14.

Douglas, J., Jr., Ma, J. and Protter, P. (1996). Numerical methods for forward--backward stochastic differential equations. <i>Ann. Appl. Probab.</i> <b>6</b> 940--968.

El Karoui, N., Peng, S. and Quenez, M. C. (1997). Backward stochastic differential equations in finance. <i>Math. Finance</i> <b>7</b> 1--72.

Ma, J., Protter, P., San Martín, J. and Torres, S. (2002). Numerical method for backward SDEs. <i>Ann. Appl. Probab.</i> <b>12</b> 302--316.

Ma, J., Protter, P. and Yong, J. (1994). Solving forward--backward stochastic differential equations explicitly---a four step scheme. <i>Probab. Theory Related Fields</i> <b>98</b> 339--359.

Ma, J. and Yong, J. (1999). <i>Forward--Backward Stochastic Differential Equations and Their Applications.</i> <i>Lecture Notes in Math.</i> <b>1702</b>. Springer, Berlin.

Ma, J. and Zhang, J. (2002). A representation theorem for backward SDE's with non-smooth coefficients. <i>Ann. Appl. Probab.</i> <b>12</b> 1390--1418.

Ma, J. and Zhang, J. (2002). Path regularity for solutions of backward SDE's. <i>Probab. Theory Related Fields</i> <b>122</b> 163--190.

Pardoux, E. and Peng, S. (1990). Adapted solutions of backward stochastic equations. <i>System and Control Lett.</i> <b>14</b> 55--61.

Pardoux, E. and Peng, S. (1992). Backward stochastic differential equations and quasilinear parabolic partial differential equations. <i>Lecture Notes in Control and Inform. Sci.</i> <b>176</b> 200--217. Springer, Berlin.