Quantile balanced credibility model

This paper introduces a model into the methodology of greatest accuracy approach in credibility theory, we extend Pitselis (2013) quantile credibility model by including a different type of losses which is called  the weighted balanced loss function (WBLF henceforth) in order to establish novel credibility premiums under the balanced squared error loss function. More specifically, we further explain how quantiles under the WBLF can be incorporated into the classical Bühlmann’s (1967) credibility model. A new model of quantile credibility under the WBLF is presented, where the premiums are estimated using the non-parametric approach where premiums must be estimated based on data only, without postulating any type of distribution. Furthermore, we establish the credibility estimators and provide an application to real data of the results using R software to evaluate the effectiveness of our proposed model, and conclude with a comparison with the Pitselis (2013) model and the Bühlmann (1967) model to show the effectiveness of our premium.