{"title":"A novel k-generation propagation model for cyber risk and its application to cyber insurance","authors":"Na Ren, Xin Zhang","doi":"arxiv-2408.14151","DOIUrl":null,"url":null,"abstract":"The frequent occurrence of cyber risks and their serious economic\nconsequences have created a growth market for cyber insurance. The calculation\nof aggregate losses, an essential step in insurance pricing, has attracted\nconsiderable attention in recent years. This research develops a path-based\nk-generation risk contagion model in a tree-shaped network structure that\nincorporates the impact of the origin contagion location and the heterogeneity\nof security levels on contagion probability and local loss, distinguishing it\nfrom most existing models. Furthermore, we discuss the properties of\nk-generation risk contagion among multi-paths using the concept of d-separation\nin Bayesian network (BN), and derive explicit expressions for the mean and\nvariance of local loss on a single path. By combining these results, we compute\nthe mean and variance values for aggregate loss across the entire network until\ntime $t$, which is crucial for accurate cyber insurance pricing. Finally,\nthrough numerical calculations and relevant probability properties, we have\nobtained several findings that are valuable to risk managers and insurers.","PeriodicalId":501128,"journal":{"name":"arXiv - QuantFin - Risk Management","volume":"217 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuantFin - Risk Management","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.14151","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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.