Application of Constrained Bayes Estimation under Balanced Loss Function in Insurance Pricing

초록

Constrained Bayesian estimates overcome the over shrinkness toward the mean which usual Bayes and empiricalBayes estimates produce by matching first and second empirical moments; subsequently, a constrained Bayesestimate is recommended to use in case the research objectiveis to produce a histogram of the estimates considering the location and dispersion. The well-known squared error loss function exclusively emphasizes the precision of estimationand may lead to biased estimators. Thus, the balanced loss function is suggested to reflect both goodness offit and precision of estimation. In insurance pricing, the accurate location estimates of risk and also dispersionestimates of each risk group should be considered under proper loss function. In this paper, by applying thesetwo ideas, the benefit of the constrained Bayes estimates and balanced loss function will be discussed; in addition, application effectiveness will be proved through an analysis of real insurance accident data.

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