Risk Modelling and Management in Insurance

我未来5年的研究计划可以概括为采用和发展保险统计模型和计算统计方法。该计划将涵盖4个项目。 1.基于Erlang的保险损失混合模型 在这个项目中，我打算为基于Erlang的多变量混合模型开发EM算法，并使用带参数的无限Erlang混合模型来模拟重尾保险损失。该方法也将适用于其他非负/非高斯混合。 2.基于隐马尔可夫模型的复合COX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，我将考虑具有相依报告延迟的标记COX过程，将其应用于可信度理论，并将其推广到总索赔的复合COX模型中，并将其应用于IBNR索赔准备金。 3.开发高效的VA投资组合风险管理计算工具 我将为典型的VA政策选择开发模型辅助抽样方法，并为VA投资组合开发更有效的嵌套模拟方案和多资产套期保值策略。将考虑进一步适用于其他与股权挂钩的保险组合(例如可变万能险)。 4.一般保险的助推方法/正向分段累加模型 该项目的目标是开发为一般保险量身定做的助推方法。 这项建议中的所有项目都具有实际意义。我将专注于为这些问题开发新的和创新的模型和方法，并提供现成的实现算法和R包。我确实预计，这项提案的研究将对保险投资组合(一般和人寿)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).