Optimal Insurance Coverage Under Bonus-Malus Contracts

The paper analyses the questions: Should - or should not - an individual customer buy insurance? And if so, what insurance coverage should he or she prefer? Unlike classical studies of optimal insurance coverage, this paper analyses these questions from a bonus-malus point of view, that is, for insurance contracts with individual bonus-malus (experience rating or no-claim) adjustments. The paper outlines a set of new statements for bonus-malus contracts and compares them with correspondingly classical statements for standard insurance contracts. The theoretical framework is an expected utility model, and both optimal coverage for a fixed premium function and pareto optimal coverage are analyzed. The paper is an extension of another paper by the author, see Holtan (1999), where the necessary insight to - and concepts of - bonus-malus contracts are outlined.

Keywords: Insurance contracts; bonus-malus; optimal insurance coverage; deductibles; utility theory; pareto optimality