Skew mixture models for loss distributions: A Bayesian approach
AbstractThe derivation of loss distribution from insurance data is a very interesting research topic but at the same time not an easy task. To find an analytic solution to the loss distribution may be misleading although this approach is frequently adopted in the actuarial literature. Moreover, it is well recognized that the loss distribution is strongly skewed with heavy tails and presents small, medium and large size claims which hardly can be fitted by a single analytic and parametric distribution. Here we propose a finite mixture of Skew Normal distributions that provides a better characterization of insurance data. We adopt a Bayesian approach to estimate the model, providing the likelihood and the priors for the all unknown parameters; we implement an adaptive Markov Chain Monte Carlo algorithm to approximate the posterior distribution. We apply our approach to a well known Danish fire loss data and relevant risk measures, such as Value-at-Risk and Expected Shortfall probability, are evaluated as well.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 51 (2012)
Issue (Month): 3 ()
Contact details of provider:
Web page: http://www.elsevier.com/locate/inca/505554
Markov chain Monte Carlo; Bayesian analysis; Mixture model; Skew-Normal distributions; Loss distribution; Danish data;
Other versions of this item:
- Bernardi, Mauro & Maruotti, Antonello & Lea, Petrella, 2012. "Skew mixture models for loss distributions: a Bayesian approach," MPRA Paper 39826, University Library of Munich, Germany.
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
- C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
- C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Bernardi, Mauro, 2013.
"Risk measures for skew normal mixtures,"
Statistics & Probability Letters,
Elsevier, vol. 83(8), pages 1819-1824.
- Bolance, Catalina & Guillen, Montserrat & Pelican, Elena & Vernic, Raluca, 2008. "Skewed bivariate models and nonparametric estimation for the CTE risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 386-393, December.
- Marin, Jean-Michel & Mengersen, Kerrie & Robert, Christian P., 2005. "Bayesian Modelling and Inference on Mixtures of Distributions," Economics Papers from University Paris Dauphine 123456789/6069, Paris Dauphine University.
- Francesco Lagona & Marco Picone, 2012. "Model-based clustering of multivariate skew data with circular components and missing values," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 927-945, September.
- Burnecki, Krzysztof & Misiorek, Adam & Weron, Rafal, 2010. "Loss Distributions," MPRA Paper 22163, University Library of Munich, Germany.
- David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika van der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639.
- Eling, Martin, 2012. "Fitting insurance claims to skewed distributions: Are the skew-normal and skew-student good models?," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 239-248.
- Ahn, Soohan & Kim, Joseph H.T. & Ramaswami, Vaidyanathan, 2012. "A new class of models for heavy tailed distributions in finance and insurance risk," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 43-52.
- Loperfido, Nicola, 2014. "A note on the fourth cumulant of a finite mixture distribution," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 386-394.
- Mauro Bernardi & Ghislaine Gayraud & Lea Petrella, 2013. "Bayesian inference for CoVaR," Papers 1306.2834, arXiv.org, revised Nov 2013.
- Bernardi, Mauro, 2012.
"Risk measures for Skew Normal mixtures,"
39828, University Library of Munich, Germany.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If references are entirely missing, you can add them using this form.