The paper solves the loss reserving problem using Kalman recursions in linear statespace models. In particular, if one orders claims data from run-off triangles to time series with missing observations, then state space formulation can be applied for projections or interpolations of IBNR (Incurred But Not Reported) reserves. Namely, outputs of the corresponding Kalman recursion algorithms for missing or future observations can be taken as the IBNR projections. In particular, by means of such recursive procedures one can perform effectively simulations in order to estimate numerically the distribution of IBNR claims which may be very useful in terms of setting and/or monitoring of prudency level of loss reserves. Moreover, one can generalize this approach to the multivariate case of several dependent run-off triangles for correlated business lines and the outliers in claims data can be also treated effectively in this way. Results of a numerical study for several sets of claims data (univariate and multivariate ones) are presented.

中文翻译：

---

将状态空间模型应用于随机索赔保留

本文使用线性状态空间模型中的卡尔曼递归解决了损失保留问题。特别是，如果一个命令要求数据从径流三角形到缺少观测的时间序列，那么状态空间公式可以应用于 IBNR 的投影或插值 (发生但未报告) 储备金。即，对应的卡尔曼递归算法的缺失或未来观测的输出可以作为 IBNR 投影。特别是，通过这种递归程序，人们可以有效地执行模拟，以便在数字上估计 IBNR 索赔的分布，这在设置和/或监控损失准备金的审慎水平方面可能非常有用。此外，可以将这种方法推广到相关业务线的多个依赖径流三角形的多元情况，并且也可以通过这种方式有效地处理索赔数据中的异常值。给出了几组索赔数据（单变量和多变量数据）的数值研究结果。