Credibility Premium Under Relative Loss Function

The classical B\"uhlmann credibility formula estimates the hypothetical mean of a particular insured, or risk by square error loss. However, the ratio of the charged premium and the true premium is more appropriate to measure equity of the premium than the absolute value of their difference. Regarding to this case, we propose two alternative loss functions to calculate the credibility premium in this paper. The one combines the squared error loss and the relative loss ratio is called as therelative mean square error loss. The other one mixes the relative entropy loss function instead of the squared error loss is called as the relative entropy loss function. The estimation method of credibility factors and their properties are investigated.