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

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  • Dong, A.X.D.
  • Chan, J.S.K.

Abstract

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.

Suggested Citation

  • Dong, A.X.D. & Chan, J.S.K., 2013. "Bayesian analysis of loss reserving using dynamic models with generalized beta distribution," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 355-365.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:2:p:355-365
    DOI: 10.1016/j.insmatheco.2013.07.001
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    Cited by:

    1. Avanzi, Benjamin & Taylor, Greg & Vu, Phuong Anh & Wong, Bernard, 2020. "A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 50-71.
    2. Boratyńska, Agata, 2017. "Robust Bayesian estimation and prediction of reserves in exponential model with quadratic variance function," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 135-140.
    3. Alice X. D. Dong & Jennifer S. K. Chan & Gareth W. Peters, 2014. "Risk Margin Quantile Function Via Parametric and Non-Parametric Bayesian Quantile Regression," Papers 1402.2492, arXiv.org.
    4. Ceren Eda Can & Gul Ergun & Refik Soyer, 2022. "Bayesian Analysis of Proportions via a Hidden Markov Model," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3121-3139, December.
    5. Benjamin Avanzi & Gregory Clive Taylor & Phuong Anh Vu & Bernard Wong, 2020. "A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving," Papers 2004.06880, arXiv.org.
    6. Li, Zhengxiao & Wang, Fei & Zhao, Zhengtang, 2024. "A new class of composite GBII regression models with varying threshold for modeling heavy-tailed data," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 45-66.
    7. Gareth W. Peters, 2018. "General Quantile Time Series Regressions for Applications in Population Demographics," Risks, MDPI, vol. 6(3), pages 1-47, September.
    8. Gareth W. Peters & Wilson Ye Chen & Richard H. Gerlach, 2016. "Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-Moments," Risks, MDPI, vol. 4(2), pages 1-41, May.
    9. Erengul Dodd & George Streftaris, 2017. "Prediction of settlement delay in critical illness insurance claims by using the generalized beta of the second kind distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(2), pages 273-294, February.
    10. Gareth W. Peters & Wilson Y. Chen & Richard H. Gerlach, 2016. "Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-moments," Papers 1603.01041, arXiv.org.
    11. Chan Jennifer So Kuen & Ng Kok-Haur & Nitithumbundit Thanakorn & Peiris Shelton, 2019. "Efficient estimation of financial risk by regressing the quantiles of parametric distributions: An application to CARR models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(2), pages 1-22, April.

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