Credibility Models And Their Applications Under The Balanced Loss Function

Traditional actuarial science is generally limited to the field of life insurance, and it originally forms and develops into life actuarial. Yet, due to the rapid development of information technology, especially since the WWII, began to establish the risk theory for the non-life insurance. It makes the non-life insurance actuarial technology gradually matures, and now forms the non-life actuarial.The development of non-life actuarial science is far later than life actuarial science. There are some specific reasons why the problems of non-life actuarial quantitative analysis are more complex. Up to now, it has developed two important sections, loss distribution theory and risk theory.Firstly, based on square loss function in credibility theory, we introduce the penalty function and establish an asymmetry balanced loss function by weighting method. Secondly, under the new balanced function, combined with Buhlmann credibility and Buhlmann-Straub credibility methods, we catch credibility premiums estimation which is a linear expression. It is fairly easy to calculate and strong to apply. Finally, under Buhlmann credibility model, with non-parametric method and Poisson semi-parametric method and Normal-Normal parametric method, we have credibility estimation for credibility factor and claim frequency. We also provide empirical research and analysis.