Bootstrapping individual claim histories.

*(English)*Zbl 1277.62259Summary: The bootstrap method BICH is given for estimating mean square prediction errors and predictive distributions of non-life claim reserves under weak conditions. The dates of claim occurrence, reporting and finalization and the payment dates and amounts of individual finalized historic claims form a claim set from which samples with replacement are drawn. We assume that all claims are independent and that the historic claims are distributed as the object claims, possibly after inflation adjustment and segmentation on a background variable, whose distribution could have changed over time due to portfolio change. Also we introduce the new reserving function RDC, using all these dates and payments for reserve predictions. We study three reserving functions: chain ladder, the Schnieper (1991) method and RDC. Checks with simulated cases obeying the assumptions of T. Mack [ibid. 29, No. 2, 361–366 (1999; Zbl 1277.62256)] for chain ladder and H. Liu and R. Verrall [ibid. 39, No. 1, 35–60 (2009; Zbl 1205.91087)] for Schnieper’s method, respectively, confirm the validity of our method. BICH is used to compare the three reserving functions, of which RDC is found overall best in simulated cases.