相对损失函数下的倍度保费(英文)

Credibility Premium Under Relative Loss Function

传统的倍度保费公式利用均方损失函数估计特定保人的风险．然而,索取保费与真实保费之间的比例比它们差的绝对值更适合于衡量保费的公平性．基于这一点,我们提出了两种计算保费的损失函数:均方相对损失函数和熵相对损失函数,并且给出了倍度因子的估计公式及它们的性质．

The classical Biihlmann 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 the relative 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.