本文开篇介绍了可测空间中期望的定义，总结了经典概率论中期望的性质。然后开始引入非线性期望，在此基础上提出了一般的非线性期望 g-期望，总结了 g-期望的定义与原理。之后本文对风险度量的研究方法进行了研究，提出一般的风险度量方法为 VaR 方法。但是 VaR 并不能满足实际金融活动中影响因素的不确定性，接着在这样的背景下本文引出 g-期望下的 VaR 模型，并通过结果比较得出非线性期望在面对不确定因素与风险时有着更好的预测性。

This paper introduces the de?nition of expectation in measurable space and summarizes the properties of expectation in classical probability theory.Then the nonlinear expectation is introduced. On this basis, the general nonlinear expectation G - expectation is proposed, and the de?nition and principle of g - expectation are summarized.After that, this paper studies the research methods of risk measurement and puts forward the general risk measurement method as VaR method.However, VaR cannot satisfy the uncertainty of in?uencing factors in actual ?nancial activities. Then, in this context, this paper introduces the VaR model under G-expectation, and concludes that nonlinear expectation has better predictability in the face of uncertainties and risks through comparison of results.