On Bayesian premium credibility: maximum entropy prior for unknown claims process and numerical example

Abstract

In the complex field of insurance, determining the credibility of the most efficient premium is a major challenge, especially when the distribution of claims remains unknown. This study uses a Bayesian methodology to address this issue. In this framework, the initial assumptions concerning the unidentified parameters of the claims process are expressed by means of a distribution function. The objective is to establish premium credibility by maximizing the insurance company's expected utility while respecting specific constraints. By applying the maximum entropy method, we can derive the posterior distribution of the loss process from the observed data available. This approach is advantageous because it offers modeling flexibility and enables estimates to be progressively updated as new data becomes available. It is also particularly useful in situations where data is limited or incomplete, as is often the case in the insurance sector. The study highlights the characteristics and advantages of this Bayesian method. It highlights how the approach handles uncertainty and integrates prior knowledge into the estimation process. In addition, several numerical illustrations are included to demonstrate the practical application of the method and its impact on determining premium credibility. In summary, this research offers an innovative perspective on risk management in the insurance sector. It proposes a method that not only adheres to the playful approach to risk management, but also to the premium credibility approach.