NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS

作     者：PENG Shige 

作者机构：School of Mathematics and System ScienceShandong UniversityJinan 250100China 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2005年第26卷第2期

页      面：159-184页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：Project supported by the National Natural Science Foundation of China(No.10131040) 

主　　题：Backward stochastic differential equations Nonlinear expectation Non-linear expected utilities Measure of risk g-expectation Nonlinear Mar-kov chain g-martingale Nonlinear martingale Nonlinear Kolmogorov’s consistent theorem Doob-Meyer decomposition 

摘      要：This paper deals with nonlinear expectations. The author obtains a nonlinear gen- eralization of the well-known Kolmogorov’s consistent theorem and then use it to con- struct ?ltration-consistent nonlinear expectations via nonlinear Markov chains. Com- pared to the author’s previous results, i.e., the theory of g-expectations introduced via BSDE on a probability space, the present framework is not based on a given probabil- ity measure. Many fully nonlinear and singular situations are covered. The induced topology is a natural generalization of Lp-norms and L∞-norm in linear situations. The author also obtains the existence and uniqueness result of BSDE under this new framework and develops a nonlinear type of von Neumann-Morgenstern representation theorem to utilities and present dynamic risk measures.