Dynamic structural percolation model of loss distribution for cyber risk of small and medium-sized enterprises for tree-based LAN topology

Jevtic, Petar; Lanchier, Nicolas

doi:10.1016/j.insmatheco.2020.02.005

Cited by 26 publications

(48 citation statements)

References 13 publications

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“…Under the assumption of a tree-based local area network (LAN) topology, Jevti and Lanchier [ 17 ] present a structural model of aggregate cyber loss distribution for small- and medium-sized businesses. Hua and Xu [ 18 ] proposed a risk-spreading and recovering algorithm for generating synthetic data.…”

Section: Introductionmentioning

confidence: 99%

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

2021

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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.

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Section: Introductionmentioning

confidence: 99%

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

2021

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“…Indeed, the first moment of the size of the percolation clusters on finite graphs is closely related to the notion of network resilience in computer network theory [7]. Similarly, the modeling framework introduced by [5] shows that, in the context of cyber security, both the first and the second moments of the cluster size are keys to computing insurance premiums. Motivated by these aspects, [6] studied the first and second moments of the cluster size on elementary graphs: the path, the ring and the star.…”

Section: Introductionmentioning

confidence: 99%

First and second moments of the size distribution of bond percolation clusters on regular graphs

Lanchier¹,

Salle²

2021

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Motivated by network resilience and insurance premiums in the context of cyber security, we derive universal upper bounds for the first and second moments of the size of bond percolation clusters on finite regular graphs. Thinking of the clusters as dynamical objects coupled with branching processes gives a first set of bounds that are accurate when the probability of an edge being open is small. Estimating the number of isolated vertices, we also obtain a second set of bounds that are accurate when the probability of an edge being closed is small. As an illustration, we apply our results to the first three Platonic solids.

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“…According to The Institute of Risk Management, cyber risk is "any risk of financial loss, disruption or damage to the reputation of an organization from some sort of failure of its information technology systems" [18]. Following [10], we define cyber risk due to a data breach as "the risk of a financial loss caused by a breach of an institution's IT infrastructure by unauthorized parties, resulting in exploitation, taking possession of, or disclosure of data assets". Cyber risk has attracted considerable attention within the past years due to the rapidly growing number of cyber attacks [22].…”

Section: Introductionmentioning

confidence: 99%

“…Antonio and Indratno (2021) also used an epidemic model on regular networks to simulate the process of a virus spreading and calculating the total loss [4]. However, none of these models fully utilize the aspect of cyber resilience, which is very much connected with bond percolation [10,11].…”

Section: Introductionmentioning

confidence: 99%

“…The dynamical model designed in [10] consists of several components, including a bond percolation process, to calculate the aggregate loss resulting from consecutive cyber attacks on a tree based local area network of small and midsize enterprises. The percolation process assumes that the contagion spreads through the edges of the network with a fixed probability, thus modeling a static cyber security environment.…”

Section: Introductionmentioning

confidence: 99%

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Exact insurance premiums for cyber risk of small and medium-sized enterprises

Chiaradonna¹,

Lanchier²

2021

Preprint

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As cyber attacks have become more frequent, cyber insurance premiums have increased, resulting in the need for better modeling of cyber risk. Toward this direction, Jevtić and Lanchier (2020) proposed a dynamic structural model of aggregate loss distribution for cyber risk of small and medium-sized enterprises under the assumption of a tree-based localarea-network topology that consists of the combination of a Poisson process, homogeneous random trees, bond percolation processes, and cost topology. Their model assumes that the contagion spreads through the edges of the network with the same fixed probability in both directions, thus overlooking a dynamic cyber security environment implemented in most networks, and their results give an exact expression for the mean of the aggregate loss but only a rough upper bound for the variance. In this paper, we consider a bidirectional version of their percolation model in which the contagion spreads through the edges of the network with a certain probability moving toward the lower level assets of the network but with another probability moving toward the higher level assets of the network, which results in a more realistic cyber security environment. In addition, our mathematical approach is quite different and leads to exact expressions for both the mean and the variance of the agregate loss, and therefore an exact expression for the insurance premiums.

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Dynamic structural percolation model of loss distribution for cyber risk of small and medium-sized enterprises for tree-based LAN topology

Cited by 26 publications

References 13 publications

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

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

First and second moments of the size distribution of bond percolation clusters on regular graphs

Exact insurance premiums for cyber risk of small and medium-sized enterprises

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