The Optimal Deductible for Credibility Prediction in Non-Life Insurance

Determining the optimal deductible is a key issue in non-life actuarial science. This paper employs credibility theory and Bayesian methods to provide Bayesian forecasts and credibility predictions for future claims in insurance with deductibles, and calculates the mean squared prediction error of the credibility predictions. Based on the principle of minimizing mean squared prediction error, the paper explores how to determine the optimal deductible. Finally, numerical calculations are used to verify the existence and determination process of the optimal deductible.