Extended conditional G-expectations and related stopping times  

作　　者：Mingshang Hu Shige Peng 

机构地区：[1]Zhongtai Securities Institute for Financial Studies,Shandong University,Jinan 250100,Shandong,China [2]School of Mathematics,Shandong University,Jinan 250100,Shandong,China

出　　处：《Probability, Uncertainty and Quantitative Risk》2021年第4期369-390,共22页概率、不确定性与定量风险（英文）

基　　金：National Key R&D Program of China(Grant No.2018YFA0703900);the National Natural Science Foundation of China(Grant No.11671231);Shige Peng is supported by the Tian Yuan Projection of the National Natural Science Foundation of China(Grant Nos.11526205 and 11626247);the National Basic Research Program of China(973 Program)(Grant No.2007CB814900(Financial Risk)).

摘　　要：In this paper,we extend the definition of conditional G-expectation to a larger space on which the dynamical consistency still holds.We can consistently define,by taking the limit,the conditional G-expectation for each random variable X,which is the downward limit(respectively,upward limit)of a monotone sequence (Xi) in L_(G)^(1)(Ω).To accomplish this procedure,some careful analysis is needed.Moreover,we present a suitable definition of stopping times and obtain the optional stopping theorem.We also provide some basic and interesting properties for the extended conditional G-expectation.

关 键 词：G-EXPECTATION Conditional G-expectation Stopping times Optional stopping theorem 

分 类 号：O17[理学—数学]