Risk Prioritization in Actuarial Risk Management

我的研究目标是开发科学合理的量化工具，用于保险和风险管理领域的复杂应用。我提议的研究是通过四个广泛的研究计划，为精算风险管理开发和研究创新的风险优先战略：(I)最优再保险模型；(Ii)基于基差风险的最优对冲；(Iii)指数跟踪；以及(Iv)投资组合保险。通过严谨的数学工具和完善的优化框架，我提出的研究计划推动了风险管理科学的发展。这项研究是及时的，也是保险公司和其他金融机构的重大兴趣，因为它在风险管理科学中提供了最佳战略和指导。*第一个研究项目的主要目标是建立理论上有意义和实用的最优再保险模型，并推导出它们的解析解。这项研究有望大大推进最优再保险的科学研究，加深我们对再保险作为一种有效的风险管理工具的理解。第二个研究计划的主要目标是在一个理论上合理的框架内制定最优解决方案，以全面解决和量化基本风险，特别是关注动态环境，这显著增加了问题的复杂性。第三个研究项目旨在开发新的、计算效率高的指数跟踪程序。这项研究不仅对投资组合和基金经理至关重要，而且对精算师将基差风险降至最低也是至关重要的。最后一个研究计划的主要目标是设计具有担保特征的新的主动资产管理策略，并通过考虑各种实际重要因素来量化其表现。所建立的结果不仅有助于CPPI基金的提供者对缺口风险进行有效的评估，而且有助于投资者加深对其风险和回报权衡的理解。所有四个拟议的研究计划都将涉及培养高素质的硕士、博士和博士后人员。

The objective of my research is to develop scientifically sound quantitative tools for complex applications in the fields of insurance and risk management. My proposed research is to develop and investigate innovative risk prioritization strategies for actuarial risk management, through four broad research programs: (i) Optimal reinsurance models; (ii) Optimal hedging with basis risk; (iii) Index tracking; and (iv) Portfolio insurance. Through rigorous mathematical tools and sound optimization frameworks, my proposed research programs advance the science on risk management. The research is timely and is also of significant interest to insurance companies and other financial institutions by providing optimal strategy and guidance in the science of risk management. ******The key objective of the first research program is to develop theoretically interesting and practically useful optimal reinsurance models and derive their analytical solutions. The research is anticipated to significantly advance the scientific research on optimal reinsurance and deepen our understanding of using reinsurance as an effective risk management tool. The primary goal of the second research program is to develop optimal solutions to comprehensively addressing and quantifying the basis risk in a theoretically sound framework, especially focusing on a dynamic setting, which significantly increases the complexity of the problem. The third research program aims to develop novel and computationally efficient procedures for index tracking. The research is not only of paramount importance to the portfolio and fund managers but also actuaries in minimizing basis risk. The primary objective of the last research program is to devise new active asset management strategies with guarantee features and quantify their performance by taking into account a variety of pragmatically important factors. The established results are significantly helpful not only for the provider of a CPPI fund to conduct an effective evaluation on the gap risk, but also for the investors to deepen their understanding on their risk and reward tradeoffs. All the four proposed research programs will involve training of highly qualified personnel at the master's, PhD, as well as postdoctoral levels.