Pricing insurance premia: a top down approach

Insurance plays an important economic and social role through its ability to transfer risk. In this paper, we focus on the largest insurance sector, the automobile sector. We model automobile insurance premia through a top down approach. Our approach is appealing since it defines the dynamics of the aggregate loss in a consistent way, and also provides a coherent definition of the joint distribution of the total losses and the car insurance premium. We show how to make this top down approach computationally tractable by using the class of affine point processes, which are intensity-based jump processes driven by affine jump diffusions. An affine point process is sufficiently flexible to account for both country global infrastructure and driving behaviour. Further it allows for efficient computation and calibration of a large class of insurance products.