When constructing parametric models to predict the cost of future claims, several important details have to be taken into account: (i) models should be designed to accommodate deductibles, policy limits, and coinsurance factors, (ii) parameters should be estimated robustly to control the influence of outliers on model predictions, and (iii) all point predictions should be augmented with estimates of their uncertainty. The methodology proposed in this paper provides a framework for addressing all these aspects simultaneously. Using payment-per-payment and payment-per-loss variables, we construct the adaptive version of method of winsorized moments (MWM) estimators for the parameters of truncated and censored lognormal distribution. Further, the asymptotic distributional properties of this approach are derived and compared with those of the maximum likelihood estimator (MLE) and method of trimmed moments (MTM) estimators. The latter being a primary competitor to MWM. Moreover, the theoretical results are validated with extensive simulation studies and risk measure sensitivity analysis. Finally, practical performance of these methods is illustrated using the well-studied data set of 1500 U.S. indemnity losses. With this real data set, it is also demonstrated that the composite models do not provide much improvement in the quality of predictive models compared to a stand-alone fitted distribution specially for truncated and censored sample data.

翻译：在构建预测未来索赔成本的参数化模型时，需考虑以下重要细节：（i）模型设计应能适应免赔额、保单限额及共保系数；（ii）参数估计需具备稳健性，以控制异常值对模型预测的影响；（iii）所有点预测需辅以不确定性估计。本文提出的方法学为同时解决上述问题提供了一个统一框架。基于每笔赔付支付变量与每笔损失支付变量，我们构建了截断与删失对数正态分布参数的自适应温索化矩法（MWM）估计量。进一步推导了该方法的渐近分布性质，并与极大似然估计法（MLE）及修剪矩法（MTM）估计量进行对比——后者是MWM的主要竞争方法。此外，通过大规模模拟研究与风险度量敏感性分析验证了理论结果。最后，利用经充分研究的1500例美国补偿损失数据集，展示了各方法的实际性能。该真实数据集分析还表明，复合模型相较于单一拟合分布（尤其针对截断与删失样本数据）对预测模型质量的提升有限。