Risk Modelling and Management in Insurance

我在未来5年的研究计划可以概括为采用和开发保险统计模型和计算统计方法。该计划将涵盖四个项目 * 1.基于Erlang的混合模型的保险损失 * 在这个项目中，我打算开发EM算法的多元Erlang混合，并使用参数化的无限Erlang混合模型重尾保险损失。该方法也将适用于其他非负/非高斯混合。*2。复合考克斯模型与隐马尔可夫模型及其在损失准备金和费率制定中的应用 * 在这个项目中，我将考虑具有相关报告延迟的标记考克斯过程，将该过程应用于可信性理论，并将其扩展到复合考克斯模型，用于总索赔，并应用于IBNR索赔准备金 *。3.为VA投资组合风险管理开发有效的计算工具 * 我将开发模型辅助抽样方法，用于代表性VA政策选择，并为VA投资组合开发更有效的嵌套模拟方案和多资产对冲策略。我们会考虑进一步应用于其他股票挂钩保险组合（例如可变万能人寿）。*4。Boosting methods/forward stagewise additive models for general insurance* 本项目的目标是为一般保险开发量身定制的boosting方法。* *我将专注于为这些问题开发新的创新模型和方法，并提供现成的实现算法和R包。我确实期望本提案的研究将对保险投资组合（普通和人寿）的建模和风险管理产生重大影响。

My research program in the next 5 years may be generally described as to adopt and develop statistical models and computational statistical methods for insurance. The program will cover 4 projects.***1. Erlang-based mixture models for insurance losses***In this project, I intend to develop EM algorithms for multivariate Erlang-based mixtures, and to model heavy tailed insurance losses using parameterized infinite Erlang mixtures. The methodology will also be applied to other non-negative/non-Gaussian mixtures. ***2. Compound Cox models with HMM and its application to loss reserving and ratemaking***In this project, I will consider marked Cox processes with dependent reporting delays, apply the processes to credibility theory, and extend it to compound Cox models for aggregate claims with application in IBNR claim reserving.***3. Developing efficient computational tools for VA portfolio risk management***I will develop model-assisted sampling methods for representative VA policy selection and develop more efficient nested simulation schemes and multi-asset hedging strategies for VA portfolios. Further application to other equity-linked insurance portfolios (variable universal life (VUL) for example) will be considered. ***4. Boosting methods/forward stagewise additive models for general insurance***The objective of this project is to develop tailor-made boosting methods for general insurance. ******All the projects in this proposal are of practical importance. I will focus on developing new and innovative models and methodology for those problems, and provide ready-to-use implementation algorithms and R packages. I do expect that the research from this proposal would have a significant impact on modelling and risk management of insurance portfolios (general and life).**