Uncertainty-Based Credibility and Its Applications

This paper proposes a methodology to calculate the credibility risk premium based on the uncertainty of the risk premium (aka pure loss cost, pure premium), as estimated by the standard deviation of the risk premium estimator. An optimal estimator based on the uncertainties involved in the pricing process is constructed. The method takes into account both the uncertainty of the client risk premium and that of the market risk premium, and the correlation between them in the case that the client is part of the reference market. The methodology is especially well suited for those situations where the market information is limited and is therefore affected by significant parameter uncertainty, such as is the case in excess-of-loss reinsurance.