A Gillespie Algorithm and Upper Bound of Infection Mean on Finite Network

Indratno, Sapto Wahyu; Antonio, Yeftanus

doi:10.1007/978-981-15-0399-3_29

Cited by 3 publications

(4 citation statements)

References 18 publications

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“…The clustering coefficient metric as a function of communication weights may be a critical element to consider in determining how epidemics spread [ 44 ] in future studies. Complexity in large-scale simulations encourages the creation of more efficient algorithms, such as a modification of the Gillespie algorithm [ 35 ]. From the perspective of mathematical modeling, the theory and application of fractional differential equations [ 45 ] to risk modeling [ 46 ] or mixed fractional risk processes [ 47 ], particularly cyber risk, might be an attractive research area.…”

Section: Discussionmentioning

confidence: 99%

“…In contrast, the simulation process is run using a modified Markov-based simulation with different infection rates. In previous work, we used the average degree factor as a matrix of the network in a compartment SIS process [ 35 ]. We propose a modified Markov-based algorithm with different rates at the individual-level ε -SIS model to generate synthetic cyber-attack data in this study.…”

Section: Introductionmentioning

confidence: 99%

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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: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2021

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“…The study of epidemics and their modeling has been widely used to understand the cyber risk process and how computer viruses spread [26], [27]. Xu and Hua [28] have successfully introduced the modeling and pricing of cybersecurity insurance with a network structure approach.…”

Section: Epidemic Modelmentioning

confidence: 99%

“…The authors used a susceptible-infectious-susceptible (SIS) epidemic model with a different approach. The simulation of the SIS compartment model to predict cyber risk with the Gillespie Algorithm has been carried out for several finite networks [12]. In reference [10], the authors used the SIS model without the possibility of self-infection to capture cyber infection.…”

Section: Introductionmentioning

confidence: 99%

Adjusting cyber insurance premiums based on frequency in a communication network

Indratno

Antonio

Saputro

2021

Int. J. Adv. Intell. Informatics

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This study compares cyber insurance premiums with and without a communication network effect frequency. As a cybersecurity factor, the frequency in a communication network influences the speed of cyberattack transmission. It means that a network or a high activity node is more vulnerable than a network with low activity. Traditionally, cyber insurance pricing considers historical data to set premiums or rates. Conversely, the network security level can evaluate using the Monte Carlo simulation based on the epidemic model. This simulation requires spreading parameters, such as infection rate, recovery rate, and self-infection rate. Our idea is to modify the infection rate as a function of the frequency in a communication network. The node-based model uses probability distributions for the communication mechanism to generate the data. It adopts the co-purchase network formation in market basket analysis for building weighted edges and nodes. Simulations are used to compare the initial and modified infection rates. This paper considered prism and Petersen graph topology as case studies. The relative difference is a metric to compare the significance of premium adjustment. The results show that the premium for a node with a low level in a communication network can reach 28.28% lower than the initial premium. The premium can reach 20.99% lower than the initial network premium for a network. Based on these results, insurance companies can adjust cyber insurance premiums based on computer usage to offer a more appropriate price.

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Cyber Insurance Ratemaking: A Graph Mining Approach

Antonio

Indratno

Simanjuntak

2021

Risks

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Cyber insurance ratemaking (CIRM) is a procedure used to set rates (or prices) for cyber insurance products provided by insurance companies. Rate estimation is a critical issue for cyber insurance products. This problem arises because of the unavailability of actuarial data and the uncertainty of normative standards of cyber risk. Most cyber risk analyses do not consider the connection between Information Communication and Technology (ICT) sources. Recently, a cyber risk model was developed that considered the network structure. However, the analysis of this model remains limited to an unweighted network. To address this issue, we propose using a graph mining approach (GMA) to CIRM, which can be applied to obtain fair and competitive prices based on weighted network characteristics. This study differs from previous studies in that it adds the GMA to CIRM and uses communication models to explain the frequency of communications as weights in the network. We used the heterogeneous generalized susceptible-infectious-susceptible model to accommodate different infection rates. Our approach adds up to the existing method because it considers the communication frequency and GMA in CIRM. This approach results in heterogeneous premiums. Additionally, GMA can choose more active communications to reflect high communications contribution in the premiums or rates. This contribution is not found when the infection rates are the same. Based on our experimental results, it is apparent that this method can produce more reasonable and competitive prices than other methods. The prices obtained with GMA and communication factors are lower than those obtained without GMA and communication factors.

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A Gillespie Algorithm and Upper Bound of Infection Mean on Finite Network

Cited by 3 publications

References 18 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

Adjusting cyber insurance premiums based on frequency in a communication network

Cyber Insurance Ratemaking: A Graph Mining Approach

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