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A general multivariate chain ladder model

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  • Zhang, Yanwei

Abstract

A general multivariate stochastic reserving model is formulated, which not only specifies contemporaneous correlations, but also allows structural connections among triangles. Its structure extends the existing multivariate chain ladder models in a natural way, and this extension proves to be advantageous in improving model adequacy and increasing model flexibility. It is general in the sense that it includes various models in the chain ladder framework as special cases. At the heart of this model is the seemingly unrelated regression technique, which is utilized to estimate parameters that reflect contemporaneous correlations. The use of this technique is essential to construct flexible models, and related statistical theories are applied to study properties of existing estimators. A numerical example is utilized to show the advantage of the proposed model in studying multiple triangles that are related both structurally and contemporaneously.

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  • Zhang, Yanwei, 2010. "A general multivariate chain ladder model," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 588-599, June.
    • Handle: RePEc:eee:insuma:v:46:y:2010:i:3:p:588-599
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    1. Baltagi, Badi H., 1989. "Applications of a necessary and sufficient condition for OLS to be BLUE," Statistics & Probability Letters, Elsevier, vol. 8(5), pages 457-461, October.
    2. Braun, Christian, 2004. "The Prediction Error of the Chain Ladder Method Applied to Correlated Run-off Triangles," ASTIN Bulletin, Cambridge University Press, vol. 34(2), pages 399-423, November.
    3. Ajne, Björn, 1994. "Additivity of Chain-Ladder Projections," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 311-318, November.
    4. Henningsen, Arne & Hamann, Jeff D., 2007. "systemfit: A Package for Estimating Systems of Simultaneous Equations in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i04).
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    Cited by:

    1. Ioannis Badounas & Georgios Pitselis, 2020. "Loss Reserving Estimation With Correlated Run-Off Triangles in a Quantile Longitudinal Model," Risks, MDPI, vol. 8(1), pages 1-26, February.
    2. Himchan Jeong & Dipak Dey, 2020. "Application of a Vine Copula for Multi-Line Insurance Reserving," Risks, MDPI, vol. 8(4), pages 1-23, October.
    3. Yanwei Zhang & Vanja Dukic, 2013. "Predicting Multivariate Insurance Loss Payments Under the Bayesian Copula Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 891-919, December.
    4. Peng Shi, 2017. "A Multivariate Analysis of Intercompany Loss Triangles," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(2), pages 717-737, June.
    5. Peremans, Kris & Van Aelst, Stefan, 2018. "Robust inference for seemingly unrelated regression models," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 212-224.
    6. Kris Peremans & Stefan Van Aelst & Tim Verdonck, 2018. "A Robust General Multivariate Chain Ladder Method," Risks, MDPI, vol. 6(4), pages 1-18, September.

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