多维金融风险度量及其应用研究

本项目对金融投资组合，研究相应的多维风险度量。具体地，在公理化框架下，系统研究各种静态数量值、集合值多维风险度量的表示定理；研究各种动态数量值、集合值多维风险度量的表示定理及相应的 time-consistency 性质；构造各种具体有效的集合值多维风险度量；研究多维风险度量在资产配置、再保险风险模型的最优投资--再保险策略研究中的应用。项目涉及金融投资组合、金融风险度量、保险数学、动态规划、随机分析、随机过程、统计学等学科领域；属数学、概率论与数理统计与金融、保险的交叉研究；所获成果可望用于金融机构或金融监管机构的金融风险监控与监管、保险公司的风险监控、指导保险公司的投资决策。

This project is to study the multivariate risk measures for financial portfolios. Namely, by an axiomatic approach, this project will systematically study representation results for various static scalar and set-valued multivariate risk measures; and will systematically study representation results and the properties of time-consistency for various dynamic scalar and set-valued multivariate risk measures; Construction of various effective set-valued multivariate risk measures will also be investigated; The project will also investigate the applications to capital allocations and optimal investiment--reinsurance strategies for reinsurance risk models. The project is involved with fields such as financial portfolio, financial risk measure, insurance mathematics, dynamic programming, stochastic analysis, stochastic processes, statistics and so on. Hence, it is an interdisciplinary of mathematics, probability and statistics and finance and insurance. The achivements of this project can be used to the potential control of financial risks, insurance risks and to give directions to investment decision making of insurance companies.