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NEW LOSS RESERVE MODELS WITH PERSISTENCE EFFECTS TO FORECAST TRAPEZOIDAL LOSSES IN RUN-OFF TRIANGLES

Published online by Cambridge University Press:  21 September 2022

Farha Usman  and
Jennifer S.K. Chan
Farha Usman*
Affiliation:
School of Mathematics and Statistics University of Sydney Sydney, NSW 2006, Australia
Jennifer S.K. Chan*
Affiliation:
School of Mathematics and Statistics University of Sydney Sydney, NSW 2006, Australia
*
E-Mail: fusm0507@uni.sydney.edu.au
E-Mail: jennifer.chan@sydney.edu.au
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Abstract

Modelling loss reserve data in run-off triangles is challenging due to the complex but unknown dynamics in the claim/loss process. Popular loss reserve models describe the mean process through development year, accident year, and calendar year effects using the analysis of variance and covariance (ANCOVA) models. We propose to include in the mean function the persistence terms in the conditional autoregressive range model for modelling the persistence of claim across development years. In the ANCOVA model, we adopt linear trends for the accident and calendar year effects and a quadratic trend for the development year effect. We investigate linear or log-transformed mean functions and four distributions, namely generalised beta type 2, generalised gamma, Weibull, and exponential extension, with positive support to enhance the model flexibility. The proposed models are implemented using the Bayesian user-friendly package Stan running in the R environment. Results show that the models with log-transformed mean function and persistence terms provide better model fits. Lastly, the best model is applied to forecast partial loss reserve and calendar year reserve for three years.

Keywords

Loss reservingrun-off trianglepersistenceconditional autoregressive range modelBayesian analysisgeneralised beta type 2 distribution
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 52 , Issue 3 , September 2022 , pp. 877 - 920
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The International Actuarial Association

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