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.
Index insurance under demand and solvency constraints
CREST Laboratory, CNRS, Groupe des Écoles Nationales d’Économie et Statistique, Ecole Polytechnique, Institut Polytechnique de Paris（CREST实验室，法国国家科学研究中心，国立经济与统计学院集团，巴黎综合理工学院，巴黎理工学院）；Detralytics
A Wasserstein GAN-based climate scenario generator for risk management and insurance: the case of soil subsidence
Biostatistiques et Processus Spatiaux (BioSP), INRAE, Avignon, France（生物统计与空间过程（BioSP），法国国家农业食品与环境研究委员会（INRAE），法国阿维尼昂）；CREST, CNRS, Ecole polytechnique, Groupe ENSAE-ENSAI, ENSAE Paris, Institut Polytechnique de Paris, Palaiseau, France（法国国家科学研究中心（CNRS）、巴黎高等理工学院（École polytechnique）、ENSAE-ENSAI小组、巴黎ENSAE、巴黎理工学院（Institut Polytechnique de Paris）、法国帕莱索）；Fondation du Risque, Institut Louis Bachelier, Paris, France（风险基金会、路易·巴舍利尔研究所（Institut Louis Bachelier）、法国巴黎）
