The optimal deductible for credibility prediction in non-life insurance

The determination of the optimal deductible is an important problem in non-life insurance. In this paper, by using the credibility theory and Bayesian method, the Bayesian prediction and credibility prediction of future claims for deductible insurance are obtained. In addition, the mean square prediction error of credibility prediction is solved. Under the principle of minimum mean square prediction error, the solution of the optimal deductible is also discussed. Finally, the existence and solving process of the optimal retention are verified by numerical calculation.