基于行为金融模型的随机比较

The project is devoted to the development of stochastic comparison methods and applications based on behavioral finance model. The main contents are as follows. Firstly, in case that there exists a utility function with several convex or concave segments in empirical analysis of behavioral finance, we develop a continuum of stochastic dominance rules which covers preferences from stochastic dominance. We will investigate its relationships with utility classes and probability transfers, and study its Strassen's martingale representation theorem and so on. Secondly, based on our previous work, we use non-L-p probability metrics between the survival function of a risk X and its distortion to characterize the variability of X, and will show their properties in the sense of some popular stochastic orders and provide some applications on the premium principle. Thirdly, we will characterize some common stochastic orders and aging notions in terms of expected utilities from the comparative static results, and then will try to establish the closure properties of these stochastic orders under convolution operation. The significance of this project is to give a new research direction for stochastic comparisons from expected utility theory and to provide a better theoretical support for the actual applications in finance and insurance.

本项目主要研究基于行为金融模型的随机比较方法及应用。主要内容包括如下三个部分：(1) 考虑到行为金融实证中存在着分段凹-凸的效用函数，我们引入了涵盖随机占优风险偏好的连续随机占优法则，并将探索它与效用函数类、概率变化之间的关系，研究它的Strassen鞅表示定理和其它一些重要性质；(2) 在我们前期工作的基础上，提出使用非L-p概率距离下的扭曲波动性度量来刻画风险的波动性，并将研究它在随机序下的性质与在保险原理中的应用；(3) 从期望效用理论中的比较静态结果出发，研究风险偏好随机序和寿命分布基于期望效用的等价刻画，以发展随机比较理论中关于随机序在卷积运算下封闭这一重要性质。本项目的意义在于提供一种基于期望效用研究随机序的新方法，进一步完善随机比较理论及其在金融和保险领域中的实际应用。

本项目主要研究基于行为金融模型的随机比较方法及应用。主要内容包如下三个部分： (1) 考虑到行为金融实证中存在着分段凹-凸的效用函数，且投资者在选择投资产品时与参考点有关，我们引入了涵盖随机占优风险偏好且带参考点的分数阶随机占优法则，探索它与效用函数类、概率变化之间的关系，得到了一个简单易于处理的基于数字特征的等价刻画，并把它应用到优化投资理论中，发展了带分数阶随机占优约束的随机优化模型；(2) 把熵理论引入到风险投资领域，提出了一种叉熵（Extropy）风险度量方法，并研究了它和变分距离之间的关系；(3) 从期望效用理论中的比较静态结果出发，研究了普通随机占优序和寿命分布基于期望效用理论的等价刻画，进一步完善了随机比较理论中关于随机序在卷积运算下封闭这一重要性质。