Exotic surplus-dependent risk models and their applications

量化风险管理是保险和金融领域的一个中心话题，研究人员和从业人员寻求先进的分析工具和计算方法，以更好地识别、表征、评估、管理和缓解新出现的风险。在保险业中，对于与保险人履行未来财务义务的能力有关的偿付能力风险，开发这样的量化风险管理系统至关重要。通过发展和应用分析方法和计算方法，我提出的研究计划有望在这一研究领域做出重大贡献，研究带有扰动的盈余过程。更具体地说，我和我的研究团队将专注于以下三个主题：(1)具有盈余依赖特征的随机建模和最优设计；(2)为保险风险过程开发和分析(盈余依赖)风险度量；(3)发现可变年金的潜在应用。在主题(1)中，根据保险公司动态现金流分析的最新趋势，将设计和研究具有盈余依赖特征的风险模型，以满足保险实践中不同各方的不同需求。专题(2)研究依赖盈余的风险措施，特别侧重与减少有关的措施，以帮助更深入地了解潜在危险的特征，并协助及早发现极端风险。我们还将通过概率分析来建立破产理论和风险度量之间的联系。主题(1)和(2)的综合成果将通过创新的动态战略设计和对长期风险敞口的衡量，改进偿付能力风险的量化风险管理。本文提出的研究方案的另一个贡献是扩展了奇异风险理论和盈余依赖风险度量在可变年金定价和风险管理中的应用，这是本文的重点(3)。这项研究将为保险和金融行业的研究人员和从业者提供创新的见解，并培养准备在相关研究领域领导的HQP。

Quantitative risk management is a central topic in the fields of insurance and finance, where researchers and practitioners seek the advanced analytic tools and computational methods for better identification, characterization, assessment, management and mitigation of the emerging risks. In the insurance industry, it is of utmost importance to develop such quantitative risk management systems for the solvency risk pertaining to the insurer's ability to meet its future financial obligations. My proposed research program is expected to make significant contributions in this research field through the development and application of analytical approaches and computational methodologies in the study of surplus processes with perturbations in its trajectory. More specifically, my research team and I will concentrate on the following three themes: (1) Stochastic modeling and optimal design with surplus-dependent features; (2) Develop and analyze (surplus-dependent) risk measures for insurance risk processes; (3) Discover potential applications in variable annuities. In Theme (1), following the recent trend in the analysis of an insurer's dynamic cash flows, risk models with surplus-dependent features will be designed and examined to meet the various needs of different parties in insurance practice. Theme (2) studies the surplus-dependent risk measures with a special focus on the drawdown related measures, in order to help provide deeper insight into the characteristics of potential hazards and assist in the early detection of extreme risks. We will also build the connections between ruin theory and risk measures via probabilistic analysis. The integrated outcomes from Themes (1) and (2) will improve the quantitative risk management of solvency risk through the innovative design of dynamic strategies and measurement of the exposures over time. Another contribution of my proposed research program is to expand on the application of exotic risk theory and surplus-dependent risk measures to the pricing and risk management of variable annuity, which is the focus of Theme (3). This research will provide innovative insights for researchers and practitioners in the insurance and finance industries, and train HQP who will be prepared to lead in the related research areas.