Paper: arXiv 2408.14151

Authors: Na Ren, Xin Zhang

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.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical formulation for cyber risk propagation using Bayesian networks and marked Poisson processes to model loss distributions on tree networks. However, it lacks empirical validation using real-world cyber claims or network data, relying primarily on theoretical derivations and numerical examples.

Research Flowchart

  flowchart TD
    A[Goal: Cyber Insurance Pricing via Network Loss Modeling] --> B[Inputs: Network Topology, Security Levels & Origin Location]
    B --> C[Develop Path-Based k-Generation Contagion Model]
    C --> D[Apply Bayesian Network d-Separation & Path Analysis]
    D --> E[Derive Expressions for Mean & Variance of Aggregate Loss]
    E --> F[Outcomes: Actuarial Pricing Insights & Risk Management Strategies]

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0 of 38 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.