Numerical methods for forward-backward stochastic differential equations

Annals of Applied Probability

Volumn 6, Issue 3, 1996, Pages 940-968

  Douglas Jr , Jim ^a   Ma, Jin ^a   Protter, Philip ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

Combined characteristics and finite difference method; Euler's scheme; Forward backward stochastic differential equations; Quasilinear parabolic equations; Weak convergence

Indexed keywords

EID: 0030520557     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1034968235     Document Type: Article

References (12)

1. ANTONELLI, F. (1993). Backward-forward stochastic differential equations. Ann. Appl. Probab. 3 777-793.
2. CVITANIĆ, J. and MA, J. (1996). Hedging options for a large investor and forward-backward SDE's. Ann. Appl. Probab. 6 370-398.
3. DAVIS, P. (1975). Interpolation and Approximation. Dover, New York.
4. DOUGLAS, J., JR. (1983). Finite difference methods for two-phase incompressible flow in porous media. SIAM J. Numer. Anal. 20 681-696.
5. DOUGLAS, J., JR. and RUSSELL, T. F. (1982). Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures. SIAM J. Numer. Anal. 19 871-885.
6. DUFFIE, D. and EPSTEIN, L. G. (1992). Stochastic differential utility. Econometrica 61 353-394.
7. DUFFIE, D., GEOFFARD, P-Y. and SKIADAS, C. (1992). Efficient and equilibrium allocations with stochastic differential utility. Preprint.
8. DUFFIE, D., MA, J. and YONG, J. (1994). Black's console rate conjecture. Ann. Appl. Probab. 5 356-382.
9. GILBARG, D. and TRUDINGER, N. S. (1983). Elliptic Partial Differential Equations of Second Order. Springer, Berlin.
10. KLOEDEN, P. E. and PLATEN, E. (1992). Numerical Solution of Stochastic Differential Equations. Springer, Berlin.
11. LADYZENSKAJA, O. A., SOLONNIKOV, V. A. and URAL'CEVA, N. N. (1968). Linear and Quasilinear Equations of Parabolic Type. Amer. Math. Soc., Providence, RI.
12. 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.