一致波动性度量与风险度量及其应用

风险度量是量化风险的重要工具之一，已经广泛应用于金融和保险的风险管理中。在保险中，风险度量与保费原理密切相关，被用来确定保单合约的保费；在金融风险监管中，风险度量可以用来确定金融机构的最低资本准备金。这些在负责银行业监管委员会的 Basel的协议中有明确的要求。..本项目的研究将基于极值理论、统计相依和随机比较理论，充分考虑风险的尾部风险和尾部事件的相依性，寻找两类具有同单调可加性的一致波动性度量，进而构造具有同单调可加性的一致风险度量，研究其相关性质和刻画，给出风险度量的有效估计，最终应用于实际风险管理中。与此同时，我们还将基于随机序和效用函数的性质进行风险分布类的刻画，研究分数阶随机占优和相应的分数阶风险厌恶，探讨风险度量和不同阶风险厌恶的一致性，以及极端风险和风险组合的相依结构对风险度量的影响。..本项目的研究将有助于人们更好地认识风险度量、把握和应用风险度量。

Risk measure is one of the important tools and widely used in quantitative risk management of insurance companies and financial institutions. In insurance, risk measures have close relationships to premium principles, calculating the insurance price of a risk. In financial risk regulation, risk measures are used to determine the minimum of the required solvency capital. These were stated clearly in the documents of the Basel Committee on Banking Supervision...In this project, based on extreme values theory, statistical dependence and stochastic comparisons, we will pay more attention to capturing tail risks and dependencies from tail events of risk aggregation. We try to look for two families of coherent variability measures with comonotonic additivity, construct two families of coherent risk measures with comonotonic additivity, study their properties and characterizations, give effective estimation of these kinds of risk measures, and finally apply them in the practical risk management. Meanwhile, we will also characterize the families of risk distributions in terms of stochastic orders and utility functions, study fractional stochastic dominance and corresponding fractional risk aversion, establish the consistency between risk measures and notions of risk aversion, and investigate the impact of extreme risk and dependence structures on risk measures...This project will enable one to understand risk measures, grasp and apply risk measures.