This talk first consider the problem of computing different types of finite time survival probabilities for a Markov-Modulated risk model and a Markov-Modulated risk model with reinsurance, both with varying premium rates. We use the multinomial approximation scheme to derive an efficient recursive algorithm to compute finite time survival probabilities and finite time draw-down survival probabilities. Numerical results shows that by comparing with MCMC approximation, discretize approximation and diffusion approximation methods, the proposed scheme performs accurate results in all the considered cases and with better computation efficiency. Then this talk gives a new approximation method to get the optimal retention for a combination of quota-share and excess of loss reinsurance, also assuming that the insurer has partial information of the individual claim size.We then derive the optimal retention for the reinsurance arrangement by minimizing the approximated ruin probability. Some numerical examples are given which show that the proposed Bowers Gamma with Pade approximation performance better than translated gamma with De Vylder approximation. We also extend this numerical result to a risk model with prevention. 

报告人简介

李婧超，深圳大学数学与统计学院助理教授，澳大利亚精算师协会精算师，深圳市海外高层次人才，深圳市高层次后备级人才。获得澳大利亚墨尔本大学精算学专业学士，荣誉学士及博士学位。曾担任香港中银保险集团公司精算助理 。研究领域主要包括破产理论与风险管理，在 Insurance: Mathematics & Economics 等期刊发表论文多篇。曾主持国家自然科学基金项目，深圳市高层次人才科研启动项目，参与科技部重点研发计划子课题。