Lp weak convergence method on BSDEs with non-uniformly Lipschitz coefficients and its applications

In this paper, by using Lp ( 1 < p≤2) weak convergence method on backward stochastic differential equations (BSDEs) with non-uniformly Lipschitz coefficients, we obtain the limit theorem of g-supersolutions. As applications of this theorem, we study the decomposition theorem of Eg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathcal {E}}_{g}$\end{document}-supermartingale, the nonlinear decomposition theorem of Doob-Meyer’s type and so on. Furthermore, by using the decomposition theorem of Eg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathcal {E}}_{g}$\end{document}-supermartingale, we provide some useful characterizations of an Eg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathcal {E}}^{g}$\end{document}-evaluation by the generating function g(t;ω;y;z) without the assumption that g is continuous with respect to t. Our results generalize the known results in Ph. Briand et al., Electronic Commun. Probab.5 (2000) 101–117; L Jiang, Ann. Appl. Probab.18 (2008) 245–258; S Peng, Probab. Theory Relat. Fields113 (1999) 473–499; S Peng, Modelling derivatives pricing with their generating functions (2006) http://arxiv.org/abs/math/0605599 and E Rosazza Gianin, Insur. Math. Econ.39 (2006) 19–34.