保险精算中的一个随机模型

A STOCHASTIC MODEL FOR INSURANCE ACTUARIAL SCIENCE

本文假设投保人到达保险公司的过程是一个强度为λ（ｘ）的非齐次Ｐｏｉｓｓｏｎ 过程、在时间区间（０，ｔ］中的索赔额是一个与保险规则及在（０，ｔ］中的投保人数有关的随机变量，提出一个新的保险精算模型，获得保险公司在（０，ｔ］中盈余额的一些数字特征．经典的个体模型和短期聚合风险模型均为本模型的特殊情形．

This paper presents a new model for the insurance actuarial science.In this model,assume that insurers reach the insurance company in accordance with a nonhomogeneous Poisson process having rate λ(x) .And assume that the claim amount in (0,t] is a random variable relating to the insurance rule and the insurer number in (0,t] .Under these assumptions,we can get some numeral characteristic of surplus amount of the insurance company in (0,t] .These results will become the basis of manage prediction,risk evaluation and new insurance rule for the insurance company.It is easy to discover the classic individual model and short collective risk model are both special cases of the new model.