多维风险度量及其在再保险中的应用研究

本项目研究金融投资组合的风险度量、系统风险度量和风险度量在再保险中的应用。具体地，在公理化框架下，系统研究各类多维数量值静态风险度量和集合值静态风险度量的表示定理；系统研究各类多维数量值动态风险度量和集合值动态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多维数量值风险度量和集合值风险度量；研究各类系统风险度量的结构分解定理、表示定理及相应的time consistency性质；研究风险度量在再保险中的应用，即在各种风险度量最小化的标准下，探讨最优再保险策略。本项目涉及金融投资组合、金融数学、保险数学、概率论、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；所获成果可望应用于金融机构和金融监管部门的金融风险监控与监管，指导保险公司的再保险业务决策。

This project is to study the multivariate risk measures for financial portfolios, systemic risk measures and the application of risk measurement in reinsurance. Namely, by an axiomatic approach, this project will systematically study representation results for various static multivariate scalar and set-valued risk measures; and will systematically study representation results and the properties of time consistency for various dynamic multivariate scalar and set-valued risk measures. The construction of various effective multivariate scalar and set-valued risk measures will also be investigated. The project will also investigate the structural decomposition theorem, representation results and the corresponding time consistent properties of various system risk measures. The project will also study the applications to optimal reinsurance strategies by minimizing all kinds of risk measures. The project is involved with fields such as financial portfolios, financial mathematics, insurance mathematics, probability, statistics and so on. Hence, it is an interdisciplinary of mathematics, probability and statistics and finance and insurance. The achievements of this project can be used to the potential control of financial risks, insurance risks and to guide the reinsurance decisions of insurance companies.