Univariate Credibility as a Boundary-Value Problem, A Symbolic Green’s Function Method (Regular Case)

Current formulas in credibility theory often calculate net premium as a weighted sum of the average experience of the policyholder and the average experience of the entire collection of policyholders. Because these formulas are linear, they are easy to use. Another advantage of linear formulas is that the estimate changes a fixed amount per change in claim experience, if an insurer uses which a formal, then the policyholder can predict the change in premium. In a series of writing, Young(1997,1998,2000) apply decision theory to develop a credibility formula that minimizes a loss function that is linear combination of a squared-error term and a second-derivative term or first order term. This loss function as a variational forms, is equivalent to fourth order or second order linear differential equation, respectively. This allows us for evaluation to Green's function computation via symbolic calculation to compute details of Green's function to obtain the solution.