Exotic surplus-dependent risk models and their applications

定量风险管理是保险和金融领域的一个中心主题，研究人员和从业人员寻求先进的分析工具和计算方法，以便更好地识别、表征、评估、管理和减轻新出现的风险。在保险业中，对于与保险公司履行其未来财务义务的能力有关的偿付能力风险，开发这种定量风险管理系统是至关重要的。我提出的研究计划预计将在这一研究领域做出重大贡献，通过发展和应用分析方法和计算方法来研究其轨迹上的扰动剩余过程。更具体地说，我和我的研究团队将集中在以下三个主题上：(1)具有盈余依赖特征的随机建模和优化设计；(2)制定和分析保险风险流程的（盈余依赖的）风险措施；(3)发现可变年金的潜在应用。在主题(1)中，根据对保险公司动态现金流分析的最新趋势，将设计和检查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各种需求。主题(2)研究盈余依赖风险测度，特别关注与缩减相关的测度，以帮助更深入地了解潜在风险的特征，并协助早期发现极端风险。我们还将通过概率分析建立破产理论与风险度量之间的联系。主题(1)和(2)的综合结果将通过动态策略的创新设计和随时间变化的风险度量来改进偿付能力风险的定量风险管理。我提出的研究计划的另一个贡献是扩展了外来风险理论和盈余依赖风险测度在可变年金定价和风险管理中的应用，这是主题(3)的重点。这项研究将为保险和金融行业的研究人员和从业人员提供创新的见解，并培养HQP在相关研究领域的领导人才。

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.