Optimal reinsurance designs and related problems

我的研究兴趣在于开发有效的量化工具来评估和管理与保险和金融相关的问题中的风险。这项研究提案的主要目标是开发理论上合理而又实用的解决方案，以寻求最优的再保险。 我之前的研究项目通过关注风险度量最小化再保险模型，并利用两种重要的风险度量-在险价值和条件尾部预期，获得了一系列有趣的结果。这一研究领域的灵感来自于银行和保险公司在风险管理中突出地使用这两种风险衡量标准，以及它们在偿付能力监管中的重要作用。最优再保险设计的长期挑战之一是求解相应的优化问题的数学困难。为了绕过这一困难，我开发了一种新的基于经验的方法来分析最优再保险。这种方法直接基于经验数据建立再保险模型，它使我们能够解决一大类模型的最优再保险设计问题。 虽然已经取得了丰硕的研究成果，但仍有许多重要方向值得进一步探索。广义地讲，它们可以分为三类：(1)探索经验方法的统计性质；(2)将基于经验的方法应用于更多的再保险模型；(3)将所取得的结果推广到其他最优准则和其他再保险保费原则。我还计划对金融中的部分对冲和稳健投资组合选择进行研究，因为它们与最优再保险设计的主题密切相关。我坚信，我提议的研究将引起院士和从业者的极大兴趣。

My research interests lie in developing effective quantitative tools to evaluate and manage risks in problems related to insurance and finance. The primary objective of this research proposal is to develop theoretically sound and yet practical solutions in the quest for optimal reinsurance. My previous research program has obtained a series of interesting results by focusing on risk measure minimization reinsurance models, and by exploiting two important risk measures known as Value-at-Risk and Conditional Tail Expectation. This area of research is inspired by the prominent use of these two risk measures in risk management by banks and insurance companies, and by their important role in solvency regulation as adopted by various authorities. One of the long-lasting challenges with optimal reinsurance designs is the mathematical difficulty of solving the corresponding optimization problems. To circumvent this difficulty, I developed a new empirically-based approach for analyzing optimal reinsurance. This approach formulates the reinsurance models directly based on empirical data, and it allows us to address the optimal reinsurance designs for a wide class of models. While fruitful research results have been achieved, there are still many important directions worth further exploration. Broadly, they can be categorized into three groups: (1) exploration of the statistical properties of the empirical approach; (2) application of the empirically-based approach to more reinsurance models; (3) generalizing the results achieved to other optimality criteria and other reinsurance premium principles. I also plan to conduct research on the topics of partial hedging and robust portfolio selection in finance, as they are closely related to the topic of optimal reinsurance designs. I strongly believe that the research I am proposing will be of significant interest to both academicians and practitioners.