The Credibility Premium With Time-dependent Structure

Credibility theory is a rate premium technology that can predict the premium in the next year, which is based on historical claims data and a priori information. Suppose the risk X can be characterized by the unknown risk parameter θ, and θ can be portrayed by random variable θ whose prior distribution is π(θ). The credibility premium is defined as a linear function of the historical claims data.However, in the classical Buhlmann credibility theory, the historical claims data of different years are endued the same weight, but this kind of assumption is clearly not reasonable in practice.The main work of this paper is to study the credibility premium with time-dependent structure, so that the credibility premium obtained has the following properties:the new claims have more weight than the old ones. The detailed content of this paper includes the following sections:The first chapter, we briefly introduce the significance of this paper, the current research at home and abroad and the main content of credibility premium with time-dependent structure.The second chapter, the definition and excellent properties of the exponential premium principle broadly used in our paper are introduced.The third chapter, based on the classical credibility premium, we can use two important properties of credibility premium to calculate the credibility premium under exponential premium principle if a certain time-dependent structure and an estimation error is defined.The fourth chapter, the credibility premium under exponential premium princi-ple and two important corollaries are obtained if we combine the thought of classical credibility premium (minimizing the expected loss function) and the maximum en-tropy method.The fifth chapter, the main result of this paper is summarized and the further research in the future is proposed.