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 Choquet期望，最大(最小)期望和推广的g-期望 Choquet Expectations, Minimax Expectations and Generalized Peng's g-expectations 胡锋 HU Feng 1. 曲阜师范大学数学科学学院，曲阜，山东，2731652. 山东大学数学学院，济南，山东，250100 1. School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, 273165, P. R. China2. School of Mathematics, Shandong University, Jinan, Shandong, 250100, P. R. China 收稿日期: 2011-04-01 出版日期: 2013-08-25 DOI: 10.11845/sxjz.20130414b
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 摘要 Choquet期望和最大(最小)期望是非线性期望, 它们替代经典的数学期望被广泛地应用在经济、金融和保险中. 但是, 由于非线性, 计算它们往往非常困难. 本文首先介绍推广的Peng's g-期望及其相关性质; 然后, 给出最大(最小)期望和推广的Peng's g-期望之间的关系; 最后, 利用Peng's g-期望, 在一些合理假设下, 得到Choquet期望和最大(最小)期望是一致的. 关键词 ： Choquet期望,  最大(最小)期望,  倒向随机微分方程,  推广的Peng's g-期望 Abstract：The Choquet expectation and minimax expectation, which are nonlinear expectations, have been widely used in economics, finance and insurance as an alternative to traditional mathematical expectation. However, it is usually not easy to calculate them due to their nonlinearity. In this paper, we first introduce generalized Peng's g-expectations and study their related properties. Then we consider the relation between minimax expectations and generalized Peng's g-expectations. Furthermore, by using generalized Peng's g-expectations, we show that Choquet expectations and minimax expectations are the same under some reasonable assumptions. Key words： minimax expectation    backward stochastic differential equation (BSDE)    generalized Peng's g-expectation 基金资助:This work has been supported in part by the Natural Science Foundation of Shandong Province (No. ZR2009AL015) and the Youth Foundation of Qufu Normal University (No. XJ201111) 通讯作者: hufengqf@163.com
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