Asymptotic behaviors of stochastic reserving: Aggregate versus individual models

Asymptotic behaviors of stochastic reserving: Aggregate versus individual models

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Article ID: iaor201530453
Volume: 249
Issue: 2
Start Page Number: 657
End Page Number: 666
Publication Date: Mar 2016
Journal: European Journal of Operational Research
Authors: , ,
Keywords: financial, stochastic processes, simulation, time series: forecasting methods
Abstract:

In this paper, we investigate the asymptotic behaviors of the loss reservings computed by individual data method and its aggregate data versions by Chain‐Ladder (CL) and Bornhuetter–Ferguson (BF) algorithms. It is shown that all deviations of the three reservings from the individual loss reserve (the projection of the outstanding liability on the individual data) converge weakly to a zero‐mean normal distribution at the n equ1rate. The analytical forms of the asymptotic variances are derived and compared by both analytical and numerical examples. The results show that the individual method has the smallest asymptotic variance, followed by the BF algorithm, and the CL algorithm has the largest asymptotic variance.

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