The Credibility Premiums with Common Effects Obtained under Balanced Loss Functions

In classical credibility theory, the risks in a portfolio are assumed to be mutually independent and the premiums are derived under squared loss functions. In this paper, we develop the credibility theory under balanced loss functions with a special dependence structure among the individual risks: induced by common effect (Wen et al., 2009). To be specific, credibility premiums under balanced loss functions with common effects are derived for B\"uhlmann and B\"uhlmann-Straub credibility models.