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: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=675624
• 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.

与2007-2008年金融危机一样，我们经历了完整的繁荣与萧条周期：危机前的经济泡沫、市场的突然崩盘以及危机后的衰退。金融危机不仅对全球经济造成巨大损害，也对保险金融领域的量化风险管理实践产生了广泛影响。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，以更好地表征和衡量这些极端风险。 **拟议的研究将系统地研究回撤、占领时间和巴黎时间（DOP），它们作为描述和衡量崩溃和萧条的极端风险的自然模型。由于路径依赖的特点，DOP能够提供有关保险业务或投资组合在一段时间内的表现的更可靠和更全面的信息。然后，及时做出风险管理决策至关重要。此外，最近的许多研究表明，DOP 在对保险和金融领域的各种事件、工具和法规进行建模方面具有广泛的应用。**本研究的目标是 (1) 在理论分析和研究方面发展基础理论和一般方法。 DOP的数值计算； (2) 更好地了解崩溃和萧条等极端风险； (3)改进定量风险管理技术，衡量和降低极端风险。拟议的研究每年将产生 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领域的顶级期刊上。研究生和优秀本科生将深入参与这项拟议的研究计划。