A novel k-generation propagation model for cyber risk and its application to cyber insurance

The frequent occurrence of cyber risks and their serious economic consequences have created a growth market for cyber insurance. The calculation of aggregate losses, an essential step in insurance pricing, has attracted considerable attention in recent years. This research develops a path-based k-generation risk contagion model in a tree-shaped network structure that incorporates the impact of the origin contagion location and the heterogeneity of security levels on contagion probability and local loss, distinguishing it from most existing models. Furthermore, we discuss the properties of k-generation risk contagion among multi-paths using the concept of d-separation in Bayesian network (BN), and derive explicit expressions for the mean and variance of local loss on a single path. By combining these results, we compute the mean and variance values for aggregate loss across the entire network until time $t$, which is crucial for accurate cyber insurance pricing. Finally, through numerical calculations and relevant probability properties, we have obtained several findings that are valuable to risk managers and insurers.