Loss Models: From Data to Decisions, 4th Edition

17.2 Limited fluctuation credibility theory

This branch of credibility theory represents the first attempt to quantify the credibility problem. This approach was suggested in the early nineteen hundreds in connection with workers compensation insurance. The original paper on the subject was by Mowbray in 1914 [79]. The problem may be formulated as follows. Suppose that a policyholder has experienced X_j claims or losses² in past experience period j, where j {1,2,3, …, n}. Another view is that X_j is the experience from the jth policy in a group or from the jth member of a particular class in a rating scheme. Suppose that E(X_j) = ξ, that is, the mean is stable over time or across the members of a group or class.³ This quantity would be the premium to charge (net of expenses, profits, and a provision for adverse experience) if only we knew its value. Also suppose Var(X_j) = σ², again, the same for all j. The past experience may be summarized by the average = n⁻¹(X₁ +…+ X_n). We know that E() = ξ, and if the X_j are independent, Var() = σ²/n. The insurer’s goal is to decide on the value of ξ. ...