Filtration-consistent nonlinear expectations and related g-expectations

Probability Theory and Related Fields

Volumn 123, Issue 1, 2002, Pages 1-27

  Coquet, François ^a   Hu, Ying ^a   Mémin, Jean ^a   Peng, Shige ^b  

^a UNIVERSITÉ DE RENNES 1   (France)

^b SHANDONG UNIVERSITY   (China)

Author keywords

BSDE; Doob Meyer decomposition; g martingale; Nonlinear expectation; Nonlinear martingale

Indexed keywords

EID: 0036016204     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400100172     Document Type: Article

References (12)

1. Briand, P., Coquet, F., Hu, Y., Mémin, J., Peng, S.: A converse comparison theorem for BSDEs and related properties of g-expectations, Electron. Comm. Probab, 5, 101-117 (2000)
2. Chen, Z.: A property of backward stochastic differential equations, C.R. Acad. Sci. Paris Sér. I Math. 326(4), 483-488 (1998)
3. Chen, Z., Epstein, L.: Ambiguity, Risk and Asset Returns in Continuous Time, Preprint (1999)
4. Chen, Z., Peng, S.: Continuous Properties of g-martingales, Chinese Ann. Math. Ser B 22, 115-128 (2001)
5. Chen, Z., Peng, S.: A general downcrossing inequality for g-martingales, Statist. Probab. Lett. 46(2), 169-175 (2000)
6. Duffie, D., Epstein, L.: Stochastic differential utility, Econometrica 60(2), 353-394 (1992)
7. El Karoui, N., Kapoudjian, C., Pardoux, E., Peng, S., Quenez, M.-C.: Reflected Solutions of Backward SDE and Related Obstacle Problems for PDEs, Ann. Probab. 25(2), 702-737 (1997)
8. El Karoui, N., Peng, S., Quenez, M.-C.: Backward stochastic differential equation in finance, Math. Finance 7(1), 1-71 (1997)
9. Pardoux, E., Peng, S.: Adapted solution of a backward stochastic differential equation, Systems and Control Letters 14(1), 55-61 (1990)
10. Peng, S.: A generalized dynamic programming principle and Hamilton-Jacobi-Bellman equation, Stochastics stoch. reports 38(2), 119-134 (1992)
11. Peng, S.: BSDE and related g-expectation, in Pitman Research Notes in Mathematics Series, no. 364, "Backward Stochastic Differential Equation", Ed. by N. El Karoui & L. Mazliak, 141-159 (1997)
12. Peng, S.: Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob-Meyer's type, Prob. Theory Rel. Fields 113(4), 473-499 (1999)