广义指数保费原理中风险保费的统计推断

Statistical Inferences of Risk Premium under the Generalized Exponential Premium Theory

指数保费原理是非寿险精算中的一种重要保费原理.本文提出一种改进的指数保费原理,这种保费原理不仅能包含指数保费原理作为特殊情况,而且是Esscher保费原理和净保费原理的推广,具有很多保费原理的优良性质.我们研究了这种保费原理下风险保费的极大似然估计、非参数估计和贝叶斯估计,讨论了估计的渐近无偏性、相合性和渐近正态性,并给出了渐近置信区间.最后,通过数值模拟的方法比较了几个估计的收敛速度.结论表明,在样本容量较小的情况下,非参数估计具有较小的均方误差.

The principle of exponential premium is an important premium principle in non-life actuarial science.This paper proposes an improved exponential premium principle.This premium principle can not only include the principle of exponential premium as a special case,but also the generalizations of Esscher premium principle and net premium principle,which has many excellent properties as a premium principle.We study the maximal likelihood estimates,nonparametric estimates and Bayesian estimation of risk premium,and discuss the statistical properties including asymptotic unbiased,coincidence,and asymptotic normality.In addition,the asymptotic confidence interval for this risk premium is given.Finally,the convergence rate of maximum likelihood estimation and nonparametric estimation is compared by numerical simulation method.The results show that the nonparametric estimation has a small mean square error when the sample size is small.