Bernardi, Mauro and Maruotti, Antonello and Lea, Petrella (2012): Skew mixture models for loss distributions: a Bayesian approach.
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Abstract
The 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 ValueatRisk and Expected Shortfall probability, are evaluated as well.
Item Type:  MPRA Paper 

Original Title:  Skew mixture models for loss distributions: a Bayesian approach 
Language:  English 
Keywords:  Markov chain Monte Carlo, Bayesian analysis, mixture model, SkewNormal distributions, Loss distribution, Danish data 
Subjects:  C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C11  Bayesian Analysis: General C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  40883 
Depositing User:  Mauro Bernardi 
Date Deposited:  28. Aug 2012 10:13 
Last Modified:  23. Apr 2015 09:08 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/40883 
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Skew mixture models for loss distributions: a Bayesian approach. (deposited 04. Jul 2012 12:29)
 Skew mixture models for loss distributions: a Bayesian approach. (deposited 28. Aug 2012 10:13) [Currently Displayed]