De Pril递推算法在个体风险推广模型中的应用

摘要

基于现实生活中威胁生命安全事件的增多,建立了适用于寿险研究中的个体风险推广模型,解决了个体风险在保单数量较多时风险模型应用的局限性.为了简化个体风险推广模型在实际问题中的计算过程,选取了在风险模型中有重要应用的De Pril递推近似方法.给出了个体风险推广模型的De Pril递推公式替代计算方法及误差分析结果.得到结论为总理赔金额S的De Pril递推公式一阶近似为复合Poisson过程,并给出了De Pril递推公式一阶近似时,总理赔金额的各阶原点矩表达式.最后将上述结论应用到个体风险推广模型破产概率的研究中,针对该模型在理赔分布服从指数分布情况下,进行了数值分析与图形描述,从而能更直观的观察出各参数对破产概率的影响.%The individual risk application model is built which is suitable to life insurance research due to the increasing safety accidents threatening life in real life,solving the problem that individual risk applica-tion limitation in risk model with a lot of insurance policies.De Pril recursive approximation method with important application in risk model is selected so as to simplify calculating process of individual risk model used in practice.It is concluded after De Pril recursion formula of individual risk application model replaces calculation method and error analysis result,which is:total compensated sum S ,its De Pril recursion for-mula 1st order is similar to recombination process,so when De Pril recursion formula 1st order is similar, each order origin moment of total compensated sum is given.Finally,the above conclusion is applied to the research of individual risk application model ruin probability,with the situation that this model complies with index distribution under claims settlement distribution,we conducted numerical analysis and graphic presentation,so that we can observe the effect of each parameter on ruin probability directly.