Claims modeling is a classical actuarial task aimed to understand the claim distribution given a set of risk factors. Yet some risk factors may be subject to misrepresentation, giving rise to bias in the estimated risk effects. Motivated by the unique characteristics of real health insurance data, we propose a novel class of two-part aggregate loss models that can (a) account for the semi-continuous feature of aggregate loss data, (b) test and adjust for misrepresentation risk in insurance ratemaking, and (c) incorporate an arbitrary number of correctly measured risk factors. The unobserved status of misrepresentation is captured via a latent factor shared by the two regression models on the occurrence and size of aggregate losses. For the complex two-part model, we derive explicit iterative formulas for the expectation maximization algorithm adopted in parameter estimation. Analytical expressions are obtained for the observed Fisher information matrix, ensuring computational efficiency in large-sample inferences on risk effects. We perform extensive simulation studies to demonstrate the convergence and robustness of the estimators under model misspecification. We illustrate the practical usefulness of the models by two empirical applications based on real medical claims data.

索赔建模是一项经典的精算任务，旨在了解给定一组风险因素的情况下的索赔分布。但是，某些风险因素可能会出现错误的表述，从而导致估计的风险影响存在偏差。根据实际健康保险数据的独特特征，我们提出了一种新颖的两部分式总损失模型，该模型可以（a）解释总损失数据的半连续特征，（b）测试并调整以下情况下的虚假陈述风险：保险费率制定；以及（c）包含任意数量的正确测量的风险因素。通过两个回归模型在总损失的发生和大小上共享的潜在因素，可以捕捉到未被观察到的虚假陈述状态。对于复杂的两部分模型，我们推导了参数估计中采用的期望最大化算法的显式迭代公式。为观察到的Fisher信息矩阵获得了解析表达式，从而确保了在大样本推断风险影响时的计算效率。我们进行了广泛的仿真研究，以证明在模型错误指定情况下估计量的收敛性和鲁棒性。我们通过基于实际医疗索赔数据的两个经验应用来说明该模型的实际有用性。