Competitive insurance pricing with complete information, loss-averse utility and finitely many policies

In a recent paper, Ramsay and Oguledo (2012) show that in a competitive insurance market with complete information about individuals' accident probabilities and production costs, which are proportional to the amount of insurance purchased and to the premium charged, only individuals whose accident probability is in a medium range are insurable and desire insurance. The purpose of this paper is to complement the analysis of Ramsay and Oguledo by considering production costs which are proportional to the number of policies offered by an insurer. In addition to the result of Ramsay and Oguledo we show that the group of individuals who obtain insurance is partitioned into several subgroups, where each subgroup is offered the same insurance policy. To derive this result we introduce the concept of incentive compatibility which ensures that an individual has no incentive to buy another policy. Assuming that individuals have loss-averse utility, we fully characterize the boundaries of these subgroups as the result of an undercutting process in premiums between the insurers.