Pricing of cyber insurance premiums using a Markov-based dynamic model with clustering structure

Abstract

Cyber insurance is a risk management option to cover financial losses caused by cyberattacks. Researchers have focused their attention on cyber insurance during the last decade. One of the primary issues related to cyber insurance is estimating the premium. The effect of network topology has been heavily explored in the previous three years in cyber risk modeling. However, none of the approaches has assessed the influence of clustering structures. Numerous earlier investigations have indicated that internal links within a cluster reduce transmission speed or efficacy. As a result, the clustering coefficient metric becomes crucial in understanding the effectiveness of viral transmission. We provide a modified Markov-based dynamic model in this paper that incorporates the influence of the clustering structure on calculating cyber insurance premiums. The objective is to create less expensive and less homogenous premiums by combining criteria other than degrees. This research proposes a novel method for calculating premiums that gives a competitive market price. We integrated the epidemic inhibition function into the Markov-based model by considering three functions: quadratic, linear, and exponential. Theoretical and numerical evaluations of regular networks suggested that premiums were more realistic than premiums without clustering. Validation on a real network showed a significant improvement in premiums compared to premiums without the clustering structure component despite some variations. Furthermore, the three functions demonstrated very high correlations between the premium, the total inhibition function of neighbors, and the speed of the inhibition function. Thus, the proposed method can provide application flexibility by adapting to specific company requirements and network configurations.

Modeling and management of cyber risk: a cross-disciplinary review

“…Lastly, epidemic models are implemented to characterize the propagation of the risk. The works cited in this survey come from a diverse range of journals, primarily from the fields of computer science and actuarial science, while some are from statistics (Mishra & Pandey, 2014;Liu et al, 2016a;Peng et al, 2017Peng et al, , 2018 and natural science (Gil et al, 2014;Antonio et al, 2021).…”

“…The Markov-based model developed by Xu and Hua (2019) is enriched by Antonio et al (2021), who introduce a clustering coefficient factor into the SIS process with nonzero exogenous infection rates. The network structure is characterized by the individual-level clustering coefficients, which influence the efficiency of epidemic spreading.…”

Cyber Insurance Premium Setting for Multi-Site Companies under Risk Correlation

“…Again, the model allows for the computation of losses, but no approach is taken for pricing. An inhomogeneous SIS model, which also accounts for the presence of clusters where the infection propagates faster, is considered by Antonio et al (2021). The insurance premium is said to have been computed using the utility principle and the standard deviation premium principle, but no further details are given.…”

An Overview of Security Breach Probability Models

“…That proposal has been advocated by Rosson et al (2019) in the context of the power sector. While these approaches assume loss to be known (or at least estimated), Antonio et al (2021) have proposed to incorporate the network structure into pricing to account for the presence of clusters in the diffusion of attacks. Lopez and Thomas (2022) have analyzed the possible use of parametric insurance, where a parameter related to the loss is employed instead of the true loss to determine compensation; the parametric approach allows setting up insurance policies when the amount of information about risk is limited.…”