标题:Nonlinear expectations and nonlinear Markov chains
作者:Peng, SG
通讯作者:Peng, S(peng@sdu.edu.cn)
作者机构:[Peng, S] School of Mathematics and System Science, Shandong University, Jinan 250100, China
会议名称:BSDE Conference 2002
会议日期:AUG 29-SEP 02, 2002
来源:数学年刊B辑(英文版)
出版年:2005
卷:26
期:2
页码:159-184
DOI:10.1142/S0252959905000154
关键词:Backward stochastic differential equations;Nonlinear expectation;Nonlinear expected utilities;Measure of risk;g-expectation;Nonlinear Markov chain;g-martingale;Nonlinear martingale;Nonlinear Kolmogorov\'s consistent theorem;Doob-Meyer decompositio
摘要:This paper deals with nonlinear expectations. The author obtains a nonlinear generalization of the well-known Kolmogorov\'s consistent theorem and then use it to construct filtration-consistent nonlinear expectations via nonlinear Markov chains. Compared 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 probability 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.
收录类别:CPCI-S;CSCD;SCOPUS;SCIE
WOS核心被引频次:43
Scopus被引频次:42
资源类型:会议论文;期刊论文
原文链接:https://www.scopus.com/inward/record.uri?eid=2-s2.0-20744446139&doi=10.1142%2fS0252959905000154&partnerID=40&md5=64d325c5ea27c88942afd3952921fb6c
TOP