Martingale representation theorem for theG-expectation

Stochastic Processes and their Applications - Tập 121 - Trang 265-287 - 2011
H. Mete Soner1,2, Nizar Touzi3, Jianfeng Zhang4
1ETH Swiss Federal Institute of Technology, Zurich, Switzerland
2Swiss Finance Institute, Switzerland
3CMAP, Ecole Polytechnique, Paris, France
4University of Southern California, Department of Mathematics, United States

Tài liệu tham khảo

Cheridito, 2005, The multi-dimensional super-replication problem under Gamma constraints, Annales de l’Institut Henri Poincaré, Série C: Analyse Non-Linéaire, 22, 633 Cheridito, 2007, Second order BSDE’s and fully nonlinear PDE’s, Communications in Pure and Applied Mathematics, 60, 1081, 10.1002/cpa.20168 L. Denis, M. Hu, S. Peng, Function spaces and capacity related to a sublinear expectation: application to G-Brownian motion paths, February 2008, arXiv:0802.1240. Denis, 2006, A theoretical framework for the pricing of contingent claims in the presence of model uncertainty, Annals of Applied Probability, 16, 827, 10.1214/105051606000000169 El Karoui, 1988, Controle de Processus de Markov, vol. 1321, 508 El Karoui, 1997, Reflected solutions of backward SDE’s, and related obstacle problems for PDE’s, The Annals of Probability, 25, 702, 10.1214/aop/1024404416 El Karoui, 1997, Backward stochastic differential equations in finance, Mathematical Finance, 7, 1, 10.1111/1467-9965.00022 Fleming, 1993, vol. 25 Karandikar, 1995, On pathwise stochastic integration, Stochastic Processes and Their Applications, 57, 11, 10.1016/0304-4149(95)00002-O Karatzas, 1998 Krylov, 1987 Neveu, 1975 M. Nutz, Random G-expectations, 2010, preprint. Pardoux, 1990, Adapted solution of a backward stochastic differential equation, Systems Control Letters, 14, 55, 10.1016/0167-6911(90)90082-6 Peng, 1999, Monotonic limit theory of BSDE and nonlinear decomposition theorem of Doob Meyer type, Probability Theory and Related Fields, 113, 473, 10.1007/s004400050214 S. Peng, G-expectation, G-Brownian motion, and related stochastic calculus of Itô type, 2007, arXiv:math/0601035v2. S. Peng, G-Brownian motion and dynamic risk measure under volatility uncertainty, 2007, arXiv:0711.2834v1. Soner, 2000, Super-replication under Gamma constraint, SIAM Journal on Control and Optimization, 39, 73, 10.1137/S0363012998348991 H.M. Soner, N. Touzi, J. Zhang, Quasi-sure stochastic analysis through aggregation, 2009, arXiv:1003.4431v1. H.M. Soner, N. Touzi, J. Zhang, Dual formulation of second order target problems, 2009, arXiv:1003.6050. H.M. Soner, N. Touzi, J. Zhang, Well-posedness of second order backward SDEs, 2009, arXiv:1003.6053v1. Y. Song, Some properties on G-evaluation and its applications to G-martingale decomposition, 2010, arxiv.org/abs/1001.2802v2. Xu, 2009, Martingale characterization of G-Brownian motion, Stochastic Processes and their Applications, 119, 232, 10.1016/j.spa.2008.02.001