Backward stochastic dynamics on a filtered probability space

Annals of Probability

Volumn 39, Issue 4, 2011, Pages 1422-1448

  Liang, Gechun ^a   Lyons, Terry ^b   Qian, Zhongmin ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80051655222     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/10-AOP588     Document Type: Article

References (40)

1. ANTONELLI, F. (1993). Backward-forward stochastic differential equations. Ann. Appl. Probab. 3 777-793.
2. ANTONELLI, F. and MA, J. (2003). Weak solutions of forward-backward SDE's. Stoch. Anal. Appl. 21 493-514.
3. BALLY, V., PARDOUX, E. and STOICA, L. (2005). Backward stochastic differential equations associated to a symmetric Markov process. Potential Anal. 22 17-60. MR2127730
4. BARLES, G., BUCKDAHN, R. and PARDOUX, E. (1997). Backward stochastic differential equations and integral-partial differential equations. Stochastics Stochastics Rep. 60 57-83.
5. BISMUT, J. M. (1973). Analyse convexe et probabilitiés. These, faculté des sciences de Paris, Paris.
6. BISMUT, J.-M. (1976). Théorie probabiliste du contrôle des diffusions. Mem. Amer. Math. Soc. 4 1-130.
7. BISMUT, J.-M. (1978). An introductory approach to duality in optimal stochastic control. SIAM Rev. 20 62-78.
8. p solutions of backward stochastic differential equations. Stochastic Process. Appl. 108 109-129.
9. BRIAND, P. and HU, Y. (2006). BSDE with quadratic growth and unbounded terminal value. Probab. Theory Related Fields 136 604-618.
10. BRIAND, P. and HU, Y. (2008). Quadratic BSDEs with convex generators and unbounded terminal conditions. Probab. Theory Related Fields 141 543-567. MR2391164
11. BUCKDAHN, R. and ENGELBERT, H. J. (2007). On the continuity of weak solutions of backward stochastic differential equations. Teor. Veroyatn. Primen. 52 190-199.
12. BUCKDAHN, R., ENGELBERT, H. J. and RǍŞCANU, A. (2004). On weak solutions of backward stochastic differential equations. Teor. Veroyatn. Primen. 49 70-108.
13. CHERIDITO, P., SONER, M., TOUZI, N. and VICTOIR, N. (2007). Second order backward stochastic differential equations and fully non-linear parabolic PDEs. Comm. Pure Appl. Math. 60 1081-1110.
14. CVITANÍC, J. and KARATZAS, I. (1996). Backward stochastic differential equations with reflection and Dynkin games. Ann. Probab. 24 2024-2056.
15. DUFFIE, D. and EPSTEIN, L. G. (1992). Stochastic differential utility. With an appendix by the authors and C. Skiadas. Econometrica 60 353-394.
16. EL KAROUI, N., HAMADENE, S. and MATOUSSI, A. (2009). BSDEs and Applications. Indifference Pricing: Theory and Applications. Princeton Univ. Press, Princeton, NJ. 267-320.
17. EL KAROUI, N., KAPOUDJIAN, C., PARDOUX, E., PENG, S. and QUENEZ, M. C. (1997). Reflected solutions of backward SDE's, and related obstacle problems for PDE's. Ann. Probab. 25 702-737.
18. EL KAROUI, N. andMAZLIAK, L., eds. (1997). Backward Stochastic Differential Equations. Pitman Research Notes in Mathematics Series 364. Longman, Harlow.
19. EL KAROUI, N., PENG, S. andQUENEZ, M. C. (1997). Backward stochastic differential equations in finance. Math. Finance 7 1-71.
20. GILBARG, D. and TRUDINGER, N. S. (2001). Elliptic Partial Differential Equations of Second Order. Springer, Berlin.
21. HAMADENE, S., LEPELTIER, J. P. and MATOUSSI, A. (1997). Double barrier backward SDEs with continuous coefficient. In Backward Stochastic Differential Equations (Paris, 1995-1996). Pitman Research Notes in Mathematics Series 364 161-175. Longman, Harlow.
22. HU, Y., IMKELLER, P. and MÜLLER, M. (2005). Utility maximization in incomplete markets. Ann. Appl. Probab. 15 1691-1712.
23. HU, Y. and PENG, S. (1995). Solution of forward-backward stochastic differential equations. Probab. Theory Related Fields 103 273-283.
24. KOBYLANSKI, M. (2000). Backward stochastic differential equations and partial differential equations with quadratic growth. Ann. Probab. 28 558-602.
25. KOHLMANN, M. and ZHOU, X. Y. (2000). Relationship between backward stochastic differential equations and stochastic controls: A linear-quadratic approach. SIAM J. Control Optim. 38 1392-1407 (electronic).
26. LEPELTIER, J. P. and SAN MARTIN, J. (1997). Backward stochastic differential equations with continuous coefficient. Statist. Probab. Lett. 32 425-430.
27. MA, J., PROTTER, P. and YONG, J. M. (1994). Solving forward-backward stochastic differential equations explicitly-a four step scheme. Probab. Theory Related Fields 98 339-359.
28. MA, J. and YONG, J. (1999). Forward-Backward Stochastic Differential Equations and Their Applications. Lecture Notes in Math. 1702. Springer, Berlin.
29. MA, J., ZHANG, J. and ZHENG, Z. (2008). Weak solutions for forward-backward SDEs-a martingale problem approach. Ann. Probab. 36 2092-2125.
30. MAJDA, A. (1984). Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables. Applied Mathematical Sciences 53. Springer, New York.
31. PARDOUX, É. and PENG, S. (1992). Backward stochastic differential equations and quasilinear parabolic partial differential equations. In Stochastic Partial Differential Equations and Their Applications (Charlotte, NC, 1991). Lecture Notes in Control and Inform. Sci. 176 200-217. Springer, Berlin.
32. PARDOUX, É. and PENG, S. G. (1990). Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14 55-61.
33. PENG, S. and WU, Z. (1999). Fully coupled forward-backward stochastic differential equations and applications to optimal control. SIAM J. Control Optim. 37 825-843.
34. PENG, S. G. (1990). A general stochastic maximum principle for optimal control problems. SIAM J. Control Optim. 28 966-979.
35. PENG, S. G. (1991). Probabilistic interpretation for systems of quasilinear parabolic partial differential equations. Stochastics Stochastics Rep. 37 61-74.
36. RONG, S. (1997). On solutions of backward stochastic differential equations with jumps and applications. Stochastic Process. Appl. 66 209-236.
37. ROUGE, R. and EL KAROUI, N. (2000). Pricing via utility maximization and entropy. Math. Finance 10 259-276.
38. TANG, S. J. and LI, X. J. (1994). Maximum principle for optimal control of distributed parameter stochastic systems with random jumps. In Differential Equations, Dynamical Systems, and Control Science. Lecture Notes in Pure and Appl. Math. 152 867-890. Dekker, New York.
39. YONG, J. (1997). Finding adapted solutions of forward-backward stochastic differential equations: Method of continuation. Probab. Theory Related Fields 107 537-572.
40. YONG, J. and ZHOU, X. Y. (1999). Stochastic Controls: Hamiltonian Systems and HJB Equations. Applications of Mathematics (New York) 43. Springer, New York.