Equitable insurance premium schemes

We analyze the equity properties of insurance premium schemes where agents are partitioned into groups with different average accident probabilities and each individual has to pay a premium according to the average probability of the group to which it belongs. In particular, we examine the question whether choosing finer partitions to define these groups generates more equitable situations than coarser groups. Though it turns out that partitioning the agents into finer groups can never be Lorenz dominated by the coarser partition, it cannot be guaranteed that finer partitions represent improvements over coarser ones except in very restrictive circumstances.