Risk Modelling and Management in Insurance

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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).**