【作者】 王华；

【导师】 余东；

【作者基本信息】 武汉科技大学 ， 概率论与数理统计， 2010， 硕士

【摘要】 在市场经济中,一切经济活动都在受着利率的影响,保险业也不例外.再加上保险本身就是一项有风险的活动,所以如何更好的规避风险,稳定经营,就成了保险公司最关心的问题.由此,学者也在逐渐探索更加符合实际的模型,从而为保险公司提供理论上的依据.本文结合目前的经济发展情况和保险业多险种的状况,考虑了常利率、通货膨胀率和利息力的影响分别建立了三个风险模型.第一个模型是考虑的是常利率和常通货膨胀率对初始资金和每次收取保费的影响下,保费收取和索赔都服从possion分布的风险模型,并且运用鞅方法得到了最终破产概率.第二个模型是在第一个模型的基础上,把单险种推广到双险种的研究,考虑索赔服从possion分布和负二项分布,得到了最终破产概率.第三个是在前两个模型基础上,考虑到保费收取和索赔额都受利息力的影响的一个模型,这个模型更加符合实际的需要,进而运用鞅分析的方法得到了破产概率和lundberg上界.更多还原

【Abstract】 In the market-oriented economy, all activities included insurance industry are being affected by interest rate. Except that, insurance is a risky activity, so Insurance Companies are concerned more about how to avoid risks and stable operation. As a result, scholars are increasingly exploring more realistic models, so as to provide a theoretical basis for the insurance company.In this text ,I built three models based on the economic development and the status of multi-line insurance, and consider the constant interest rates and the inflation rate .The first model is to consider the constant rate and constant rate of inflation, the premium and claims are confined to passion process, and the upper bound of the ruin probability by martingale approaches and the bound of lundberg were obtained.The second model is based on the first model, considering the double-type-insurance. the claims are confined to passion process and negative binomial process. And the ruin probability are obtain.The third model is based on the first two models, the claim and the premium are both impacted by the force of interest, then the upper bound of the ruin probability by martingale approaches was obtained.更多还原