损失发展因子稳定估计的非凸正则化方法
A non-convex regularization approach for stable estimation of loss development factors
摘要：
本文利用非凸正则化方法得到了保险赔款准备金中损失发展因子的稳定估计。在非凸正则化方法中，我们重点讨论了对数调整绝对偏差（LAAD）惩罚的使用，并讨论了LAAD惩罚回归模型的优化，我们证明了在温和的条件下，用坐标下降算法收敛。这样做的好处是，可以获得回归系数的相合估计量，同时又可以选择变量，这与损失发展系数的稳定估计有关。我们校准我们提出的模型使用多线保险数据集从财产和意外伤害保险公司，我们观察到报告的总损失沿事故年份和发展时期。与其他回归模型相比，我们的LAAD惩罚回归模型提供了非常有前途的结果。
英文摘要：
In this article, we apply non-convex regularization methods in order to obtain stable estimation of loss development factors in insurance claims reserving. Among the non-convex regularization methods, we focus on the use of the log-adjusted absolute deviation (LAAD) penalty and provide discussion on optimization of LAAD penalized regression model, which we prove to converge with a coordinate descent algorithm under mild conditions. This has the advantage of obtaining a consistent estimator for the regression coefficients while allowing for the variable selection, which is linked to the stable estimation of loss development factors. We calibrate our proposed model using a multi-line insurance dataset from a property and casualty insurer where we observed reported aggregate loss along accident years and development periods. When compared to other regression models, our LAAD penalized regression model provides very promising results.
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