风险测度的敏感性分析与创新算法

风险测度的敏感性刻画系统输入参数的变化对风险度量变化的影响程度，在风险管理与对冲、资本优化配置等领域有着重要的应用前景。考虑到不同风险偏好的投资者和监管部门可能使用不同的风险测度，本课题致力于研究一大类风险测度的敏感性，如一致风险测度、凸风险测度、扭曲风险测度等。由于模型的复杂性以及风险因子的多样性，常规的数值模拟算法需要消耗大量的计算，特别是对涉及嵌套模拟的问题。为提高敏感性参数计算的效率，本项目致力于研究高性能创新的模拟仿真算法，主要包括三方面的内容：(1)在统一的框架下研究风险测度的敏感性参数估计问题，并分析估计量的大样本统计性质；(2)结合多层级蒙特卡罗方法提高嵌套模拟算法的效率；(3)研究具有高阶收敛速度的拟蒙特卡罗嵌套模拟方法。本项目的预期理论成果将有力推动模拟仿真方法在金融风险度量领域的融通发展，为金融安全提供及时的模拟技术支持，具有重要的实用价值。

Sensitivities of risk measures quantify the changes of risks due to the changes of systemic input parameters, which have importantly practical scopes in risk management and hedging. By taking account to the fact that different investors and regulators may use different risk measures, this project is devoted to studying the sensitivities of a large class of risk measures, such as coherent risk measures, convex risk measures, and distort risk measures etc. Due to the complexity of the model and the diversity of the risk factors, plain numerical simulation algorithms consume a lot of computations, especially for the problems involving nested simulation. This project is devoted to studying efficient and innovative simulation-based algorithms. It includes three parts: (1) studying sensitivities estimation of risk measures under a unified framework, and analyzing the large sample statistical properties of the proposed estimators; (2) combining the multi-level Monte Carlo method to improve the efficiency of nested simulation; (3) studying quasi-Monte Carlo based nested simulation method that has higher order rate of convergence. This project is expected to facilitate the simulation-based methods in the field of risk management, and provide technical supports for financial security. It obviously has practical values.