Estimating Predictive Distributions for Loss Reserve Models

By Glenn G. Meyers

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Abstract

This paper demonstrates a Bayesian method for estimating the distribution of future loss payments of individual insurers. The main features of this method are (1) the stochastic loss reserving model is based on the collective risk model; (2) predicted loss payments are derived from a Bayesian methodology that uses the results of large, and presumably stable, insurers as its prior information; and (3) this paper tests its model on large numbers of insurers and finds that its predictions are well within the statistical bounds expected for a sample of this size. The paper concludes with an analysis of reported reserves and their subsequent development in terms of the predictive distribution calculated by this Bayesian methodology.

KEYWORDS: Reserving methods, reserve variability, uncertainty and ranges, Schedule P, suitability testing, collective risk model, Fourier methods, Bayesian estimation, hypothesis testing

ERRATA: In step 2b in the first column of page 263, to obtain the second moment of the paid loss for all accident years combined, the sum of the accident year variances should be added to the square of the sum of the accident year expected paid losses.

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Citation

Meyers, Glenn G., "Estimating Predictive Distributions for Loss Reserve Models," Variance 1:2, 2007, pp. 248-272.

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Variance is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.