Choquet expectation and Peng's g-expectation

• 成果类型: Article
• 署名作者: Chen, ZJ; Chen, T; Davison, M
• 署名单位: Shandong University; Western University (University of Western Ontario)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000001053
• 发表日期: 2005
• 页码: 1179-1199
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; expected utility; nonadditive probabilities; THEOREM; Capacities; ambiguity; RISK

摘要

In this paper we consider two ways to generalize the mathematical expectation of a random variable, the Choquet expectation and Peng's g-expectation. An open question has been, after making suitable restrictions PP to the class of random variables acted on by the Choquet expectation, for what class of expectation do these two definitions coincide? In this paper we provide a necessary and sufficient condition which proves that the only expectation which lies in both classes is the traditional linear expectation. This settles another open question about whether Choquet expectation may be used to obtain Monte Carlo-like solution of nonlinear PDE: It cannot, except for some very special cases.