Applications of Graph Theory in Territorial Ratemaking

Several strategies for modeling territorial variation in insurance rates have been employed historically, including the use of geodemographic variables for regression, clustering techniques, techniques based on raw location information (such as latitude and longitude), and traditional techniques that simply relate territories (as a categorical variable) to loss costs or similar measures to determine appropriate relativities. Given its applicability to territorial analysis, it is perhaps unusual that graph theory has been overlooked. Graph theory is the branch of mathematics that is concerned with relationships between objects, represented as graphs. Territories can be represented as nodes on a graph, connected by edges representing the strength of relationships between the territories. In this way, graph theory is ideally suited for representing territorial relationships. In this paper, we propose a novel method for territorial ratemaking based on graph theory. We also consider results using graph neural networks and compare to traditional territorial ratemaking methods alongside model interpretation and emphasizing practical considerations for actuarial applications.