再保险对带干扰Poisson风险模型破产时间的影响

The Influence of Reinsurance on Bankruptcy Time of Poisson Risk Model with Diffusion

联系现实中保险公司的经营行为,建立一类理赔额受限的带干扰Po isson风险模型,运用鞅论的方法,分析再保险方式对该风险模型资金盈余首次到达0时刻的影响,得到它的矩母函数和数学期望,并通过与不采用再保险方式的带Po isson风险模型资金盈余首次到达0的期望时间的比较,发现再保险方式是分散保险公司经营风险的非常有效的一种途径。

According to business practice of insurance companies, a kind of Poisson risk model with diffusion with claim limitation was established. By martingale method the influence of reinsurance ways on the time of company＇s surplus funds firstly reaching zero was analyzed. Its generation function and mathematical expectation were obtained. By comparison with the time of company＇s surplus funds firstly reaching zero for the risk model without reinsurance it was found that reinsurance is a very effective way for insurance companies to disperse risk.