Optimal Loss Financing under Bonus-Malus Contracts

The paper analyses the question: Should an insurance customer carry an occurred loss himself, or should he make a claim to the insurance company? This question is important within bonus-malus contracts with individual experience adjustments of the premium. The analysis model includes a bonus hunger strategy where the customers prefer the most profitable financial alternative, that is, the alternative which represents the lowest rate of interest. Hence the loss of bonus after a claim is calculated as a rate of interest paid from the customer to the insurer. Within this model the paper outlines the existence of a true compensation function and a relative cost function for each customer. A set of properties for bonus-malus contracts are presented and discussed. A concrete example of a bonus-malus system and an insurance compensation function illustrates the theoretical framework in a practical manner.