Backward stochastic differential equations with jumps and related non-linear expectations

Stochastic Processes and their Applications

Volumn 116, Issue 10, 2006, Pages 1358-1376

  Royer, Manuela ^a  

^a UNIVERSITÉ LYON 1   (France)

Author keywords

Backward stochastic differential equations; Doob Meyer decomposition; Jumps; Non linear expectation

Indexed keywords

BROWNIAN MOVEMENT; FILTRATION; NONLINEAR EQUATIONS; POISSON EQUATION; RANDOM PROCESSES; STOCHASTIC CONTROL SYSTEMS;

BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS; DOOB MEYER DECOMPOSITION; EQUATION PATH JUMPS; NON LINEAR EXPECTATION;

DIFFERENCE EQUATIONS;

EID: 33747892052     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2006.02.009     Document Type: Article

References (15)

1. Barles G., Buckdahn R., and Pardoux E. Backward stochastic differential equations and integral-partial differential equations. Stoch. Stoch. Rep. 60 1-2 (1997) 57-83
2. Chen Z., and Peng S. Continuous properties of g-martingales. Chinese Ann. Math. Ser. B 22 1 (2001) 115-128
3. Coquet F., Hu Y., Mémin J., and Peng S. Filtration-consistent nonlinear expectations and related g-expectations. Probab. Theory Related Fields 123 (2002) 1-27
4. Dellacherie C., and Meyer P.-A. Probabilités et Potentiel (1975), Hermann, Paris (Chapitres I à IV)
5. El Karoui N., Kapoudjian C., Pardoux E., Peng S., and Quenez M.-C. Reflected solutions of backward SDE's, and related obstacle problems for PDE's. Ann. Probab. 25 2 (1997) 702-737
6. El Karoui N., Peng S., and Quenez M.-C. Backward stochastic differential equations in finance. Math. Finance 7 1 (1997) 1-71
7. Elliott R.J. Stochastic calculus and applications. Appl. Math. vol. 18 (1982), Springer-Verlag, New York
8. Jacod J., and Shiryaev A.N. Limit theorems for stochastic processes. Grundlheren Math. Wiss. vol. 288 (1987), Springer-Verlag, Berlin, Heidelberg, New York
9. Pardoux E. Generalized discontinuous backward stochastic differential equations. In: El Karoui N., and Mazliak L. (Eds). Backward Stochastic Differential Equations. Pitman Res. Notes Math. Ser. vol. 364 (1997), Longman, Harlow 207-219
10. Pardoux E., and Peng S. Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14 1 (1990) 55-61
11. Peng S. Probabilistic interpretation for systems of quasilinear parabolic partial differential equations. Stoch. Stoch. Rep. 37 1-2 (1991) 61-74
12. Peng S. Backward stochastic differential equations and applications to optimal control. Appl. Math. Optim. 27 2 (1993) 125-144
13. Peng S. Backward SDE and related g-expectation. In: El Karoui N., and Mazliak L. (Eds). Backward Stochastic Differential Equations. Pitman Res. Notes Math. Ser. vol. 364 (1997), Longman, Harlow 141-159
14. Peng S. Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob-Meyer's type. Probab. Theory Related Fields 113 4 (1999) 23-30
15. Tang S., and Li X. Necessary conditions for optimal control of stochastic systems with random jumps. SIAM J. Control Optim. 32 5 (1994) 1447-1475