Bayesian analysis of loss reserving using dynamic models with generalized beta distribution

• Published in: Insurance, mathematics & economics mathematics & economics, 2013-09, Vol.53 (2), p.355-365
• Main Authors: Dong, A.X.D., Chan, J.S.K.
• Format: Article
• Language: English
• Subjects: Bayesian analysis; Bayesian method; Distribution; Dynamic models; Generalization; Generalized beta distribution; Insurance; Insurance applications; Insurance claims; Loss reserve; Mathematical functions; Mathematical models; Mixture distribution; Probability; Probability distribution; Simulation; State space model; Studies; Threshold model
• ISSN: 0167-6687; 1873-5959
• DOI: 10.1016/j.insmatheco.2013.07.001

A Bayesian approach is presented in order to model long tail loss reserving data using the generalized beta distribution of the second kind (GB2) with dynamic mean functions and mixture model representation. The proposed GB2 distribution provides a flexible probability density function, which nests various distributions with light and heavy tails, to facilitate accurate loss reserving in insurance applications. Extending the mean functions to include the state space and threshold models provides a dynamic approach to allow for irregular claims behaviors and legislative change which may occur during the claims settlement period. The mixture of GB2 distributions is proposed as a mean of modeling the unobserved heterogeneity which arises from the incidence of very large claims in the loss reserving data. It is shown through both simulation study and forecasting that model parameters are estimated with high accuracy. •We model long tail loss reserving data using a generalized beta distribution.•The models contain state space, mixture and threshold effects for irregular claims.•They provide more accurate reserves than conventional models.•They facilitate the classification of loss payment into different risk groups.•They provide companies greater insight to distinguish claims at an earlier stage.