Reflected forward-backward SDEs and obstacle problems with boundary conditions

Journal of Applied Mathematics and Stochastic Analysis

Volumn 14, Issue 2, 2001, Pages 113-138

  Ma, Jin ^a   Cvitanić, Jakša ^b  

^a PURDUE UNIVERSITY   (United States)

^b Och Spine at New York Presbyterian Hospitals   (United States)

Author keywords

American Game Option; Forward Backward Stochastic Differential Equations; Quasilinear Variational Inequalities; Viscosity Solutions

Indexed keywords

EID: 14844352406     PISSN: 10489533     EISSN: 16872177     Source Type: Journal    
DOI: 10.1155/S1048953301000090     Document Type: Article

References (18)

1. Antonelli, F., Backward-forward stochastic differential equations, The Annals of Appl. Probab. 3 (1993), 773-793.
2. Barles, G., Buckdahn, R. and Pardoux, E., BSDEs and integral-partial differential equations, Stoch. and Stoch. Reports 60 (1997), 57-83.
3. Buckdahn, R. and Hu, Y., Hedging contingent claims for a large investor in an incomplete market, Adv. in Appl. Probab. 30 (1998), 239-255.
4. Crandall, M., Ishii, H. and Lions, P.L., User's guide to the viscosity solutions of second order partial differential equations, Bull. AMS 27 (1992), 1-67.
5. Cvitanić, J. and Karatzas, I., Backward stochastic differential equations with reflection and Dynkin games, The Annals of Probab. 24 (1996), 2024-2056.
6. Cvitanić, J. and Ma, J., Hedging options for a large investor and forward-backward SDEs, The Annals of Appl. Probab. 6 (1996), 370-398.
7. Duffie, D. and Epstein, L.G., Stochastic differential utility, Econometrica 60 (1992), 353-394 (Appendix with C. Skiadas).
8. El Karoui, N., Kapoudjian, C., Pardoux, E., Peng, S. and Quenez, M.C., Reflected solutions of backward SDEs and related obstacle problems for PDEs, Ann. Probab. 25:2 (1997), 702-737.
9. Fleming, W. and Soner, H.M., Controlled Markov Processes and Viscosity Solutions, Springer-Verlag, Berlin 1993.
10. Gegout-Petit, A. and Pardoux, E., Equations différentielles stochastiques rétrogrades réfléchies dans un convexe, Stoch. and Stoch. Reports 57 (1996), 111-128.
11. Hamadene, S., Lepeltier, J.P. and Matoussi, A., Double barriers reflected backward SDEs with continuous coefficient, (1996), preprint.
12. Hu, Y. and Peng, S., Solution of a forward-backward stochastic differential equation, Probab. Theory Relat. Fields 103 (1995), 273-283.
13. Lions, P.L. and Sznitman, A.S., Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math. 37 (1984), 511-537.
14. Ma, J., Protter, P. and Yong, J., Solving forward-backward stochastic differential equations explicitly - A four step scheme, Probab. Theory Relat. Fields 98 (1994), 339-359.
15. Pardoux, E. and Peng, S., Adapted solution of a backward stochastic differential equation, Systems Control Lett. 14 (1990), 55-61.
16. Pardoux, E. and Rascanu, A., Backward stochastic differential equations with subdifferential operator and related variational inequalities, Stoch. Process. Appl. 76:2 (1998), 191-215.
17. Pardoux, E. and Tang, S., The study of forward-backward stochastic differential equations and its applications to quasilinear PDEs, (1996), preprint.
18. Yong, J., Finding adapted solutions of forward-backward stochastic differential equations-Method of continuation, Probab. Theory Relat. Fields 107 (1997), 537-572.