随机效应线性模型下的责任准备金估计

Estimation of liability reserve in linear model with random effects

利用随机效应来刻画非寿险保险中复杂的风险因素,构建了非寿险责任准备金的随机效应线性模型。结合信度理论的思想和方法,将责任准备金的估计限定在样本的线性函数中,通过最小化期望损失函数矩阵,获得准备金的最优预测。在求解过程中,利用了正交投影的相关结论,得到的估计能表达为加权和的信度形式。进而,证明了信度预测的无偏性和条件无偏性,并给出了预测的均方误差公式。最后,利用数值模拟的方法验证了估计关于参数的敏感度。

The linear model of random effect of non-life insurance reserve is proposed by adopting the random effect to describe the complex risk factors in non-life insurance.Based on the credibility theory,the estimation of liability reserve is limited to the linear function of the sample,and the optimal forecast of reserve is obtained by minimizing the expected loss function matrix.In the process of solving,the estimation can be expressed as the credibility form of weighted sum by using the related conclusions of orthogonal projection.Furthermore,the unbiasedness and conditional unbiasedness of credibility prediction are derived,and the formula of mean square error of prediction is given.Finally,the sensitivity of estimation about parameters is verified by numerical simulations.