Tool 3: The Elasticity of a Bonus-Malus System

Abstract

The main goal of the establishment of a bonus-malus system is to reduce the premium for good drivers and to increase it for bad drivers. It is often assumed that the random variables “number of claims” and “claim amount” are independent. This assumption essentially states that the cost of an accident is for the most part beyond the control of a policyholder. If someone drives too fast and skids off the road, he may end up in a tree, or he may permanently disable a senior executive, father of five young children. The cost of the accident is largely independent of the mistake that caused it. The degree of care exercised by a driver will mostly influence his number of accidents, but in a much lesser way the cost of these accidents. Bad drivers will provoke more claims, but not necessarily more expensive claims.