Analysis of first passage times with risk management applications

2007-2008年的金融危机（也称为大衰退）对保险和金融领域的风险管理实践产生了广泛的影响。设计和实施良好的风险管理做法的重要性在某些情况下得到了痛苦的证明，并被证明是保险公司能否度过最后一段金融极端不稳定时期的决定性因素。保险公司和其他重要的金融参与者已经增加了他们的风险管理活动，主要是描述新的和正在出现的威胁，定量评估这些威胁，并开发尖端技术，通过使用最新的金融工具，现代保险政策设计以及其他手段来减轻潜在的风险。此外，保险业已投入大量资源，发展更完善和综合的风险管理架构，以更好地评估保险公司的偿付能力风险。我提出的研究计划有望在这一直接研究领域做出重大贡献。一般保险风险模型的发展和随后的分析是我研究的一个中心主题。更具体地说，我建议的研究涉及保险公司的现金流动态分析，特别关注财务压力时期固有的风险。我的研究计划的核心是压力期，它开始要么是资本短缺（破产），要么是资本水平的极端负面冲击（下降）。在科学界最近趋势的基础上，将引入并进一步分析具有额外路径依赖特征的风险措施，以协助早期发现潜在风险。我的研究将导致重大进展的数学理论和相关技术的风险过程的研究。应用概率学的相关学科（如扩散理论和流体流动理论）也将受益于这些进步。这将巩固这些研究学科之间的知识转移。我提出的研究的另一个主要目标包括风险模型的发展，随后将允许适当的风险管理实践的好处的定量测量。预计将使用分析和概率技术进行上述分析。

The financial crisis of 2007-2008 (also known as the Great Recession) has had extensive impact on the practice of risk management in insurance and finance. The importance of designing and implementing good risk management practices was painfully demonstrated in some cases and shown to be a determining factor in an insurer's ability to weather the last period of extreme financial instability. Insurers and other important financial players have since increased their risk management activities by most notably characterizing new and emerging threats, quantitatively assessing these threats, and developing cutting-edge techniques to mitigate potential risks via the use of the most up-to-date financial instruments, modern design of insurance policies, as well as other means. Also, the insurance industry has since heavily invested on the development of a more sophisticated and integrated risk management framework to better assess an insurer's solvency risk. My proposed research program is expected to make significant contributions in this immediate field of research. The development and the subsequent analysis of general insurance risk models are a central theme of my research.***More specifically, my proposed research pertains to the analysis of an insurer's cash flow dynamics with a special focus on the risks inherent to periods of financial stress. Central to my research program are stress periods which begin either with a capital shortfall episode (ruin) or extreme negative shocks in capital levels (drawdown). Building on the recent trend in the scientific community, risk measures with additional path-dependent features will be introduced and further analyzed to assist in the early detection of potential risks. My research will lead to significant advances in mathematical theory and related techniques for the study of risk processes. Related disciplines in applied probability (such as queueing theory and fluid flow theory) will also benefit from such advances. This will solidify the transfer of knowledge among these research disciplines. Another main objective of my proposed research consists in the development of risk models which will subsequently allow for a quantitative measurement of the benefits of proper risk management practices. Both analytic and probabilistic techniques are expected to be used to conduct the alluded analysis.**