Numerical method for backward stochastic differential equations

Annals of Applied Probability

Volumn 12, Issue 1, 2002, Pages 302-316

  Ma, Jin ^a   Protter, Philip ^b   San Martín, Jaime ^c   Torres, Soledad ^c,d  

^a PURDUE UNIVERSITY   (United States)

^b Department of Obstetrics Gynecology   (United States)

^c CNRS   (France)

^d UNIVERSIDAD DE VALPARAÍSO   (Chile)

Author keywords

Backward stochastic differential equations; Numerical methods

Indexed keywords

EID: 0036101915     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1015961165     Document Type: Article

References (16)

1. ANTONELLI, F. and KOHATSU-HIDA, A. (2000). Filtration stability of backward SDE's. Stochastic Anal. Appl. 18 11-37.
2. BALLY, V. (1997). Approximation scheme for solutions of BSDE. Backward Stochastic Differential Equations (N. El Karoui and L. Mazliak, eds.) 177-191. Pitman, London.
3. BALLY, V., PAGÈS, G. and PRINTEMS, J. (2001). A stochastic quantization method for nonlinear problems. Monte Carlo Methods Appl. 7 21-34.
4. BUCKDAHN, R. (2001). Backward stochastic differential equations driven by a martingale. Preprint 93-05, Univ. Provence.
5. CHEVANCE, D. (1997). Discrétisation des équations différentieles stochastiques rétrogrades. In Numerical Methods in Finance (L. C. G. Rogers and D. Talay, eds.) 232-244. Cambridge Univ. Press.
6. COQUET, F., MACKEVIČIUS, V. and MÉMIN, J. (1998). Stability in D of martingales and backward equations under discretization of filtration. Stochastic Process. Appl. 75 235-248.
7. DOUGLAS, J., MA, J. and PROTTER, P. (1996). Numerical methods for forward-backward stochastic differential equations. Ann. Appl. Probab. 6 940-968.
8. EL KAROUI, N., PENG, S. and QUENEZ, M. C. (1997). Backward stochastic differential equations in finance. Math. Finance 7 1-71.
9. EL KAROUI, N. and QUENEZ, M. C. (1997). Nonlinear pricing theory and backward stochastic differential equations. Financial Mathematics. Lecture Notes in Math. 1656 191-246. Springer, New York.
10. FREIDLIN, M. (1985). Functional Integration and Partial Differential Equations. Princeton Univ. Press.
11. JACOD, J., MÉMIN, J. and METIVIER, M. (1983). On tightness and stopping times. Stochastic Process. Appl. 14 109-146.
12. LEPELTIER, J. P. and SAN MARTIN, J. (1997). Backward stochastic differential equations with continuous generator. Statist. Probab. Lett. 32 425-430.
13. MA, J., PROTTER, P. and YONG, J. (1994). Solving forward-backward stochastic differential equations explicitly - a four step scheme. Probab. Theory Relat/Fields 98 339-359.
14. PARDOUX, E. and PENG, S. (1990). Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14 55-61.
15. PARDOUX, E. and PENG, S. (1992). Backward stochastic differential equation and quasilinear parabolic partial differential equations. Stochastic Partial Differential Equations and Their Applications. Lecture Notes in Control and Inform. Sci. 176 200-217. Springer, New York.
16. PROTTER, P. (1990). Stochastic Integration and Differential Equations. Springer, New York.