Path-dependent measures of risks: drawdowns, occupation times and Parisian times

路径依赖的风险度量：回撤、占领时间和巴黎时间

• 批准号: RGPIN-2014-05828
• 负责人: Li, Bin
• 金额: $ 1.09万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=657417
• 关键词: Path; dependent; measures; risks; drawdowns

As in the 2007-2008 financial crisis, we have experienced a complete cycle of booms and busts: the economic bubble before the crisis, the sudden crash of the market, as well as the recession thereafter. The financial crisis not only caused huge damage to the global economy but also had extensive impact on the practice of quantitative risk management in insurance and finance. It prompts researchers in Canada and all over the world to develop and improve mathematical models to better characterize and measure these extreme risks. **The proposed research will systematically study drawdowns, occupation times, and Parisian times (DOP) which serve as natural models to characterize and measure the extreme risks of crash and depression. Because of the features of path dependency, DOP are able to provide with more reliable and comprehensive information on the performance of insurance businesses or investment portfolios in a time period. Then, risk management decisions can be taken in a timely manner which is of paramount importance. Moreover, much of recent research has showed that DOP have wide applications in modeling various events, instruments and regulations in insurance and finance.**The objectives of this proposed research are (1) to develop fundamental theory and general methodology in both theoretical analysis and numerical computation of DOP; (2) to pursue a better understanding of extreme risks such as crash and depression; (3) to improve quantitative risk management techniques to measure and reduce the extreme risks. The proposed research will produce 2-3 sole or joint papers per year to be published in the top tier journals in actuarial science, applied probability or mathematical finance. Graduate students and exceptional undergraduate students will be intensively involved in this proposed research program.

正如2007-2008年的金融危机一样，我们经历了一个完整的繁荣和萧条的周期：危机前的经济泡沫，市场的突然崩溃，以及之后的衰退。金融危机不仅对全球经济造成了巨大的破坏，而且对保险和金融业的量化风险管理实践也产生了广泛的影响。它促使加拿大和世界各地的研究人员开发和改进数学模型，以更好地描述和衡量这些极端风险。** 拟议的研究将系统地研究提款，占领时间和巴黎时间（DOP），这些都是表征和衡量崩溃和抑郁的极端风险的自然模型。由于路径依赖的特性，DOP能够提供更可靠和全面的信息，在一个时间段内的保险业务或投资组合的表现。然后，可以及时做出风险管理决策，这是至关重要的。此外，最近的许多研究表明，DOP在保险和金融领域的各种事件、工具和法规建模中有广泛的应用。本研究的目标是：（1）发展DOP理论分析和数值计算的基础理论和一般方法;（2）更好地理解极端风险，如崩溃和抑郁症;（3）改进定量风险管理技术，以测量和降低极端风险。拟议的研究将每年产生2-3篇单独或联合论文，发表在精算科学，应用概率或数学金融的顶级期刊上。研究生和优秀的本科生将深入参与这项拟议的研究计划。