The Benktander claim reserving method, combining chain ladder method and Bornhuetter-Ferguson method using optimal credibility

Based on the settlement period for insurance claim, insurance is divided into 2 types of business which are short-tail business (settlement period <1 year) and long-tail business (settlement period ≥1 year). In long-tail business, it is important for insurance company to have claim reserve in order to settle claims in the future. Claim reserve modelling is done using chain ladder method that is based on the trend of paid claims. Another method that is often used is Bornhuetter-Ferguson which is based on paid claims and also premium. In this paper, Benktander method that combines chain ladder and Bornhuetter-Ferguson using optimal credibility is introduced. Optimal credibility is obtained through minimum mean squared error and minimum variance. Benktander provides moderate reserve compared to chain ladder and Bornhuetter-Ferguson.