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

Proceedings Mathematical Sciences

FENG HU¹  ZHAOJUN ZONG² 

[1] $$;School of Statistics, Qufu Normal University, Qufu, Shandong , China$$

关键词: Backward stochastic differential equation;    $epsilon^g$-evaluation;    $g$-expectation;    $epsilon_g$-martingale;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper, by using $L_p$ ($1 lt p leq 2$) 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 $epsilon_g$-supermartingale, the nonlinear decomposition theorem of Doob-Meyer’s type and so on. Furthermore, by using the decomposition theorem of $epsilon_g$-supermartingale, we provide some useful characterizations of an $epsilon^g$-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. {f 5} (2000) 101–117; L Jiang, Ann. Appl. Probab. {f 18} (2008) 245–258; S Peng, Probab. Theory Relat. Fields {f 113} (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. {f 39} (2006) 19–34.

【 授权许可】

Unknown