Credibility theory and Kalman filtering with extensions
R.К. Mehra · 1976
In this paper it is shown that the estimate and prediction problems considered in credibility theory are similar to those considered in Kalman filtering theory. The state vector of the risk model consists of the average risk variables such as the number of claims, cost of claims, etc. for a particular risk from the collective of risks. The observed data consists of the risk variables for the collective and for the individual risks. It is required to predict the values of risk variables in the next time period based on this data and to adjust the individual premiums based on claims experience in such a way as to converge to their true values.