复合二项分布下多险种的负风险模型

摘要

The negative multiple line risk model of discrete process was considered. Insurers' premium income was a negative constant, and claims models were compound binomial risk process. By constructing the expectations about claim process, the adjustment coefficient of definition was given. Then in line with martingale theory, the Lundberg inequality of ruin probability was concluded, furthermore, ruin probability formula and the exact formula of ruin probability were obtained by the updated theory and recursion. And the limit of ruin probability was given at the end of the paper according to the exact formula of ruin probability.%考虑了离散的复合二项分布下多险种的负风险模型.其中,保险公司的保费收入是一个负的常数,并且索赔过程为复合二项过程模型的多险种风险过程.通过构建有关索赔过程的期望方程给出了调节系数的定义,并通过鞅论得到了破产概率的Lundberg不等式(伦德伯格不等式),运用更新理论与递归的手法获得了破产概率的关系式以及破产概率确切的表达式.而且,最后根据破产概率的具体表达式给出了关于破产概率的一个极限值.