Linear Filtering and Recursive Credibility Estimation

Recursive credibility estimation is discussed from the viewpoint of linear filtering theory. A conjunction of geometric interpretation and the innovation approach leads to general algorithms not developed before. Moreover, covariance characterizations considered by other researchers drop our elegantly as a result of geometric considerations. Examples are presented of Kalman type filters valid for non-Gaussian measurements. Keywords: Credibility, filtering theory, linear Bayesian theory, geometry, Kalman filter, prospective ratemaking, Gram-Schmidt, Fourier series.