Application of compound poisson process in system reliability 复合泊松过程在系统可靠性中的应用
In this paper , we study the risk model with random premium rate and the risk model with two compound poisson processes 本文研究了保费率为随机变量的风险模型的破产概率及其精算量和双复合poisson风险模型的破产概率的估计。
About the risk model with two compound poisson processes , we discuss the risk model with two compound poisson processes and the risk model with two compound poisson processes by diffusion . then we get lundberg inequality and the formula of ruin probability in this new model 对于保费收入过程为复合poisson过程的破产模型,本文就不带干扰时的破产模型和带干扰时的破产模型进行讨论,运用鞅方法的得出了破产概率满足的lundberg不等式。
But , in most of general risk model , the premium income is a constant rate , scholar have generalized the aggregated premium income from a constant rate process to a poisson process . in this article , the author defines the model that premium income is a compound poisson process , not a constant rate process , it is named compound poisson process premium income risk model 作者建立了保费收入为复合泊松过程的风险模型,在新的风险模型中包含两个复合泊松过程,首先考察了复合泊松过程可加性的性质,据此性质,把这两个复合泊松过程化简为一个复合泊松过程,使模型得到化简。
百科解释
A compound Poisson process is a continuous-time (random) stochastic process with jumps. The jumps arrive randomly according to a Poisson process and the size of the jumps is also random, with a specified probability distribution.