In stochastic reserving, the incurred outstanding liabilities of general insurance companies result in incomplete claims because of truncation and censoring. It is necessary for insurance companies to predict liabilities in risk management. We propose a model that allows the incorporation of heterogeneity among policies, which is important for loss reserving. The incompleteness of observation data leads us to use expectation-maximization (EM) algorithm to obtain the maximum likelihood estimations of the parameters of the model. We also show that the deviation of loss reserving from the loss reserve weakly converges to a normal distribution at the rate $\sqrt{m}$, where $m$ is the size of the risk portfolio. A simulation study is conducted to compare the proposed method with the ones without policyholder’s information as well as obtained by chain ladder method and compare the convergence rates of EM algorithm and the direct maximization by Newton-Raphson method. We also analyse real-life health insurance data to illustrate the use of the method in practice.

在随机准备金中，一般保险公司发生的未偿债务由于截断和审查而导致索赔不完整。保险公司在风险管理中需要对负债进行预测。我们提出了一个模型，该模型允许在策略之间结合异质性，这对于损失准备金很重要。观测数据的不完整性导致我们使用期望最大化（EM）算法来获得模型参数的最大似然估计。我们还表明，损失准备金与损失准备金的偏差弱收敛到正态分布的速率$\sqrt{米}$， 在哪里$米$是风险组合的规模。通过仿真研究，将所提方法与没有投保人信息的方法以及链梯法得到的方法进行比较，比较了EM算法的收敛速度和Newton-Raphson方法的直接最大化。我们还分析了现实生活中的健康保​​险数据，以说明该方法在实践中的使用。