基于非可加测度的一致性变异测度

建立在经典概率测度理论体系下的风险测度理论已经有了不少的研究成果,但在金融、保险市场中存在着许多的非可加风险,针对传统风险测度理论分析非可加风险的缺陷,研究了在Choquet积分理论基础上的风险变量空间为非可加测度空间的变异测度问题,证明了这种测度是共单调可加一致性的变异测度,给出了在Chance空间共单调可加一致性变异测度的表示定理,这些结论是对风险变异测度理论在非可加条件下的发展,对于分析非可加风险具有重要的理论价值与现实意义。

The Coherent Measure of Variability Based on Nonadditive Measure

The theory of risk measurement based on the theory of classical probability measurement has already had a lot of research results,but there are many nonadditive risks in the financial and insurance markets,therefore, it is of great theoretical and practical significance to analyze the theory of risk measurement based on nonadditive measure.First, we propose one measure of variability based on the Choquet integral theory, and prove that this measure is a coherent and comonotonical additive measure of variability.Then, we give one representation and comonotonical additive measures of variability in chance space.These conclusions extend the theory of measure of variability to the nonadditive condition.