Robust Bayesian methodology with applications in credibility premium derivation and future claim size prediction

Ali Karimnezhad () and Ahmad Parsian ()

AStA Advances in Statistical Analysis, 2014, vol. 98, issue 3, 287-303

Abstract: Robust Bayesian methodology deals with the problem of explaining uncertainty of the inputs (the prior, the model, and the loss function) and provides a breakthrough way to take into account the input’s variation. If the uncertainty is in terms of the prior knowledge, robust Bayesian analysis provides a way to consider the prior knowledge in terms of a class of priors $$\varGamma $$ Γ and derive some optimal rules. In this paper, we motivate utilizing robust Bayes methodology under the asymmetric general entropy loss function in insurance and pursue two main goals, namely (i) computing premiums and (ii) predicting a future claim size. To achieve the goals, we choose some classes of priors and deal with (i) Bayes and posterior regret gamma minimax premium computation, (ii) Bayes and posterior regret gamma minimax prediction of a future claim size under the general entropy loss. We also perform a prequential analysis and compare the performance of posterior regret gamma minimax predictors against the Bayes predictors. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Bayesian analysis; Credibility premium; General entropy loss; Prequential analysis; Robust Bayesian analysis (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:spr:alstar:v:98:y:2014:i:3:p:287-303

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DOI: 10.1007/s10182-013-0222-0

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