经典风险模型中破产变量的联合分布-《深圳大学学报理工版》

文章信息/Info

Title:: The joint distribution of ruin related quantities in the classical risk model

Author(s):: SU Bihao and LI Jingchao; College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, Guangdong Province, P.R.China

Keywords:: classical risk model; time of ruin; deficit at ruin; aggregate claim amount up to ruin; number of claims up to ruin; joint probability density

摘要:: 破产理论对风险衡量和风险调控至关重要，破产索赔作为破产理论的一大重点问题，通过研究总索赔额随时间的分布，可以对风险进行较好描述．根据其分布的特征，可采取注资及保费再调整等方式进行风险调控．在经典风险模型中，优先考虑的4个破产相关变量为：破产时间、截止至破产时的总索赔额、截止至破产时的总索赔次数及破产时的赤字．本研究考虑截止至破产时的总索赔额与其他破产变量的联合概率密度函数，给出当个体索赔为指数分布时，不同联合概率密度函数的表达式．指出当个体索赔分布服从某一类特定分解形式时，联合概率密度函数的表达式也可以分解并求出．

Abstract:: Ruin theory plays a crucial role in risk measurement and risk regulation. Bankruptcy claims is a major focus of ruin theory and the distribution of the aggregate amount of claim can well describe the risk of insurance portfolio. According to the distribution characteristics, we can adopt such means as capital injection and premium re-adjustment to regulate risk. In the classical risk model, the priorities are given to four ruin-related variables: the time of ruin, the aggregate claim amount up to ruin, the total number of claims up to ruin and the deficit at ruin. In this paper, we mainly consider the joint probability density function of the aggregate claim amount up to ruin with other ruin related quantities. The explicit expressions are given for the joint densities when the individual claim follows exponential distribution. In addition, when the individual claim follows a particular decomposition form, the joint density can also be obtained in a decomposition form.