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 mislading 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 present 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 unknow 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, as Value-at-Risk and Expected Shortfall probability, are evaluated as well.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 39826.
Date of creation: 2012
Date of revision:
Markov chain Monte Carlo; Bayesian analysis; mixture model; Skew-Normal distributions; Loss distribution; Danish data;
Other versions of this item:
- Bernardi, Mauro & Maruotti, Antonello & Petrella, Lea, 2012. "Skew mixture models for loss distributions: A Bayesian approach," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 617-623.
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-07-14 (All new papers)
- NEP-ECM-2012-07-14 (Econometrics)
- NEP-RMG-2012-07-14 (Risk Management)
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.:
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"Risk measures for Skew Normal mixtures,"
39828, University Library of Munich, Germany.
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