Credibility premium plans which make allowance for bonus hunger

Abstract By “bonus-hunger” is meant the tendency of an experience rated policy holder to self-insure small damages in order to avoid an increase in future premium costs. The aim of this paper is to demonstrate, within the framework of a simple model, how fair experience rating plans can be constructed when the policy-holders hunger for bonus. In the first three sections some basic concepts of credibility theory are introduced, and specific assumptions are made concerning the risk process and the bonus-hunger strategy of the policy holders. In section 4 a credibility formula is derived which is optimal (in the sense of least squares) when the bonus-hunger strategy is independent of the premium system. In section 5 credibility formulas are derived in cases when the bonushunger strategy depends on the premium system, and a numerical example is given. The practical applicability of the results is discussed in section 6.