A complete representation theorem for G-martingales

Stochastics

Volumn 86, Issue 4, 2014, Pages 609-631

  Peng, Shige ^a   Song, Yongsheng ^b   Zhang, Jianfeng ^c  

^a SHANDONG UNIVERSITY   (China)

^b CHINESE ACADEMY OF SCIENCES   (China)

^c UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

G expectations; G martingales; martingale representation theorem; nonlinear expectations

Indexed keywords

EID: 84904327270     PISSN: 17442508     EISSN: 17442516     Source Type: Journal    
DOI: 10.1080/17442508.2013.865130     Document Type: Article

References (28)

1. P.Cheridito, H.M.Soner, N.Touzi, and N.Victoir, Second order BSDE's and fully nonlinear PDE's, Commun. Pure Appl. Math.60 (2007), pp. 1081-1110.
2. L.Denis, M.Hu, and S.Peng, Function spaces and capacity related to a sublinear expectation: Application to G-Brownian motion pathes, Potential Anal.34 (2011), pp. 139-161.
3. L.Denis and C.Martini, A theorectical framework for the pricing of contingent claims in the presence of model uncertainty, Ann. Appl. Probab.16 (2006), pp. 827-852.
4. Y.Dolinsky, M.Nutz, and H.M.Soner, Weak approximation of G-expectations, Stoch. Process. Appl.122 (2012), pp. 664-675.
5. I. Ekren, N. Touzi, and J. Zhang, Optimal stopping under nonlinear expectation, preprint, Available at arXiv:1209.6601 (2012)
6. L. Epstein and S. Ji, Ambiguous volatility, possibility and utility in continuous time, preprint, Available at arXiv:1103.1652 (2011)
7. A.Fahim, N.Touzi, and X.Waxin, A probabilitic numerical method for fully nonlinear parabolic PDEs, Ann. Appl. Probab.21 (2011), pp. 1322-1364.
8. W. Guo, J. Zhang, and J. Zhuo, A monotone scheme for high dimensional fully nonlinear PDEs, preprint, Available at arXiv:1212.0466 (2012)
9. p-Solutions for reflected backward stochastic differential equations, preprint, Available at arXiv:0807.1846 (2008)
10. M. Hu, S. Ji, S. Peng, and Y. Song, Backward stochastic differential equations driven by G-Brownian motion, preprint, Available at arXiv:1206.5889 (2012)
11. Y. Hu and S. Peng, Some estimates for martingale representation under G-expectation, preprint, Available at arXiv:1004.1098 (2010)
12. A.Matoussi, D.Possamai, and C.Zhou, Second order reflected backward stochastic differential equations, Ann. Appl. Probab., in press, Available at arXiv:1201.0746 (2012)
13. M.Nutz, Random G-expectations, Ann. Appl. Probab., in press, Available at arXiv:1009.2168 (2010)
14. M.Nutz and H.M.Soner, Superhedging and dynamic risk measures under volatility uncertainty, SIAM J. Control Optim.50 (2012), pp. 2065-2089.
15. M.Nutz and R.Van Handel, Constructing sublinear expectations on path space, Stoch. Process. Appl.123 (2013), pp. 3100-3121.
16. M. Nutz and J. Zhang, Optimal stopping under adverse nonlinear expectation and related games, preprint, Available at arXiv:1212.2140 (2012)
17. S.Peng, Filtration consistent nonlinear expectations and evaluations of contingent claims, Acta Math. Appl. Sin.20 (2004), pp. 191-214.
18. S.Peng, G-Expectation, G-Brownian motion and related stochastic calculus of Itô's type, in Stochastic Analysis and Applications: The Abel Symposium 2005, Benth, et al., eds., Abel Symposia, Springer-Verlag, Berlin Heidelberg, 2006, pp. 541-567.
19. S. Peng, Nonlinear expectations and stochastic calculus under uncertainty, preprint, Available at arXiv:1002.4546 (2010)
20. S.Peng, Backward Stochastic Differential Equation, Nonlinear Expectation and their Applications, Proceedings of the International Congress of Mathematicians 2010, Hyderabad, India2010, pp. 393-432.
21. T. Pham and J. Zhang, Some norm estimates for semimartingales - Under linear and nonlinear expectations, preprint, Available at arXiv:1107.4020v1 (2011)
22. M.Soner, N.Touzi, and J.Zhang, Martingale representation theorem under G-expectation, Stoch. Process. Appl.121 (2011), pp. 265-287.
23. M.Soner, N.Touzi, and J.Zhang, The wellposedness of second order backward SDEs, Probab. Theory Relat. Fields153 (2012), pp. 149-190.
24. M.Soner, N.Touzi, and J.Zhang, Dual formulation of second order target problems, Ann. Appl. Probab.23 (2013), pp. 308-347.
25. Y.Song, Some properties on G-evaluation and its applications to G-martingale decomposition, Sci. China Math.54 (2011), pp. 287-300.
26. Y.Song, Uniqueness of the representation for G-martingales with finite variation, Electron. J. Probab.17 (2012), pp. 1-15.
27. X. Tan, Probabilistic numerical approximation for stochastic control problems, preprint (2012)
28. J.Xu and B.Zhang, Martingale characterization of G-Brownian motion, Stoch. Process. Appl.119 (2009), pp. 232-248.