带常利率和干扰项的负风险模型相关性质

Basic properties of negative risk model with constant interest and disturbance

为解决基本负风险模型与保险公司实际运营的偏差问题,在考虑了其他因素影响的前提下,建立了同时含有常利率和干扰项的负风险模型,使其更加贴近保险公司及经营性公司的实际情况.首先采用矩母函数的定义及相关性质推导了新模型的基本性质,介绍了调节系数的概念,然后利用切比雪夫不等式证明了新模型破产概率的表达式以及破产概率所满足的Lundberg上界,最后通过数值模拟,分别分析了两种因素对新模型破产概率上界的影响.结果表明:在干扰项不变的情况下,新模型的破产概率上界会随着利率的增加而减小;在利率不变的情况下,破产概率上界会随着随机因素的干扰而变大.该成果对保险公司的实际运营具有一定的指导意义.

In order to overcome the difference between the basic negative risk model and insurance companies' operation,a negative risk model with both constant interest and disturbance has been developed.The model reflexes the realities in insurance companies and other business companies.Firstly,this paper derives the properties of the new model by using the definition and properties of moment generating function,and introduces the conception of adjustment coefficient.Secondly,this paper proves the expression of ruin probability by using Chebyshev inequality and obtains the Lundberg upper bound of the new model.Finally,this paper demonstrates the effect of two factors on the new model through numerical examples.The result shows that if the disturbance is fixed,the ruin probability upper bound of the new model will be reduced as interest increase;and it will increase under the effect of disturbance when the interest is fixed.This study is useful to the insurance companies' operation.