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STOCHASTIC CLAIMS RESERVING VIA A BAYESIAN SPLINE MODEL WITH RANDOM LOSS RATIO EFFECTS

Published online by Cambridge University Press:  13 July 2017

Guangyuan Gao  and
Shengwang Meng
Guangyuan Gao*
Affiliation:
Renmin University of China, Center for Applied Statistics and School of Statistics, Room 1006, Mingde Building, 59 Zhongguancun Avenue, Haidian District, Beijing, 100872, China
Shengwang Meng
Affiliation:
Renmin University of China, Center for Applied Statistics and School of Statistics, 59 Zhongguancun Avenue, Haidian District, Beijing, 100872, China E-Mail: mengshw@ruc.edu.cn
*
E-Mail: guangyuan.gao@anu.edu.au
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Abstract

We propose a Bayesian spline model which uses a natural cubic B-spline basis with knots placed at every development period to estimate the unpaid claims. Analogous to the smoothing parameter in a smoothing spline, shrinkage priors are assumed for the coefficients of basis functions. The accident period effect is modeled as a random effect, which facilitate the prediction in a new accident period. For model inference, we use Stan to implement the no-U-turn sampler, an automatically tuned Hamiltonian Monte Carlo. The proposed model is applied to the workers' compensation insurance data in the United States. The lower triangle data is used to validate the model.

Keywords

Stochastic claims reservingtail factornatural cubic splineHamiltonian Monte CarloBayesian modeling
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 1 , January 2018 , pp. 55 - 88
Copyright
Copyright © Astin Bulletin 2017 

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