稀疏过程在一类带干扰多险种风险模型中应用

Application of Thinning Process in One Kind of Multi-type Risk Model

随着社会的进步和发展,保险公司经营的业务也随之多元化,不断增加新的险种业务以满足社会需求。同时在经营活动中,保费的收取、索赔到达过程也是复杂多变的,保单持有者也有可能退保。因此,研究具有一定实际背景的风险模型是一件有意义的工作。建立一类带干扰扩散扰动项的多险种风险模型,其保单到达过程、索赔到达过程为平稳无后效流,保单的退保过程是一个p-稀疏过程。利用鞅论方法分析模型盈余过程的性质、破产概率的解析式及其上界估计。

With the advancement and development of society, insurance company business is also diversified and new kinds of business increases to satisfy social demands. At the same time, the premium collecting and the reaching process of claims are various and complex and holders of term are possible to withdraw. Risk model study on actual background is a magnificient job. One kind of multi-type risk model with diffusion was established, where the arrival of term and the reaching process of claims follow the finite streams with independent increments, and the refunding occurrs as the p-thinning process. Method of martingale was used to analyze the analytical formula of ruin probability and its upper bound estimation.