A numerical scheme for BSDEs

Annals of Applied Probability

Volumn 14, Issue 1, 2004, Pages 459-488

  Zhang, Jianfeng ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

Backward SDEs; L Lipschitz functionals; L 2 regularity; Step processes

Indexed keywords

EID: 26844465182     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/aoap/1075828058     Document Type: Article

References (23)

1. ASMUSSEN, S., GLYNN, P. and PITMAN, J. (1995). Discretization error in simulation of one-dimensional reflecting Brownian motion. Ann. Appl. Probab. 5 875-896.
2. 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.
3. BISMUT, J. M. (1973). Théorie probabiliste du contrôle des diffusions. Mem. Amer. Math. Soc. 176.
4. BJÖRK, T. (1998). Arbitrage Theory in Continuons Time. Oxford Univ. Press.
5. BRIAND, P., DELYON, B. and MÉMIN, J. (2001). Donsker-type theorem for BSDEs. Electron. Comm. Probab. 6 1-14.
6. CHEVANCE, D. (1996). Ph.D. thesis, Univ. Provence.
7. DAI, M. and JIANG, L. (2000). On path-dependent options. In Mathematical Finance - Theory and Applications (J. Yong and R. Cont, eds.) 290-316. Higher Education Press, China.
8. DOUGLAS, J., Jr., MA, J. and PROTTER, P. (1996). Numerical methods for forward-backward stochastic differential equations. Ann. Appl. Probab. 6 940-968.
9. EL KAROUI, N. and MAZLIAK, L. (1997). Backward Stochastic Differential Equations. Longman, Harlow.
10. EL KAROUI, N., PENG, S. and QUENEZ, M. C. (1997). Backward stochastic differential equations in finance. Math. Finance 7 1-72.
11. GIKHMAN, I. I. and SKOROHOD, A. V. (1972). Stochastic Differential Equations. Springer, New York.
12. KARATZAS, I. and SHREVE, S. E. (1987). Brownian Motion and Stochastic Calculus. Springer, New York.
13. KLOEDEN, P. E. and PLATEN, E. (1992). Numerical Solution of Stochastic Differential Equations. Springer, New York.
14. MA, J., PROTTER, P., SAN MARTÍN, J. and TORRES, S. (2002). Numerical method for backward SDEs. Ann. Appl. Probab. 12 302-316.
15. MA, J., PROTTER, P. and YONG, J. (1994). Solving forward-backward stochastic differential equations explicitly - a four step scheme. Probab. Theory Related Fields 98 339-359.
16. MA, J. and YONG, J. (1999). Forward-Backward Stochastic Differential Equations and Their Applications. Lecture Notes in Math. 1702. Springer, Berlin.
17. MA, J. and ZHANG, J. (2002). A representation theorem for backward SDE's with non-smooth coefficients. Ann. Appl. Probab. 12 1390-1418.
18. MA, J. and ZHANG, J. (2002). Path regularity for solutions of backward SDE's. Probab. Theory Related Fields 122 163-190.
19. NUALART, D. (1995). The Malliavin Calculus and Related Topics. Springer, New York.
20. PARDOUX, E. and PENG, S. (1990). Adapted solutions of backward stochastic equations. System and Control Lett. 14 55-61.
21. PARDOUX, E. and PENG, S. (1992). Backward stochastic differential equations and quasilinear parabolic partial differential equations. Lecture Notes in Control and Inform. Sci. 176 200-217. Springer, Berlin.
22. ZHANG, J. (2001). Some fine properties of backward stochastic differential equations. Ph.D. dissertation, Purdue Univ.
23. ZHANG, Y. and ZHENG, W. (2001). Discretizing a backward stochastic differential equations. Preprint.