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We develop statistical methodology for the quantification of risk of source-destination pairs in an internet network. The methodology is developed within the framework of functional data analysis and copula modeling. It is summarized in the form of computational algorithms that use bidirectional source-destination packet counts as input. The usefulness of our approach is evaluated by an application to real internet traffic flows and via a simulation study. [ABSTRACT FROM AUTHOR]

We explore the economics of ransomware on production supply chains. Integrated supply chains result in a mutual-dependence between firms that can be exploited by cyber-criminals. For instance, we show that by targeting one firm in the network the criminals can potentially hold multiple firms to ransom. Overlapping security systems may also allow the criminals to strike at weak points in the network. For instance, it may be optimal for the attacker to target a supplier in order to ransom a large producer at the heart of the production network. We introduce a game theoretic model of an attack on a supply chain and solve for two types of Nash equilibria. We then study a hub and spoke example before providing simulation results for a general case. We find that the total ransom the criminals can demand is increasing in the average path length of the network. Thus, the ransom is lowest for a hub and spoke network and highest for a line network. Mitigation strategies are discussed. [ABSTRACT FROM AUTHOR]

Correlation in cyber risk represents an additional source of concern for utility and industrial infrastructures, where risks may be introduced by connected systems. A major means of reducing risk is to transfer it through insurance. In this paper, we consider a company which has peripheral branches in addition to its headquarters, where risk correlation is present between all of its sites and insurance is adopted to hedge against economic losses. We employ the expected utility principle (which leads to the well-known mean variance premium formula) to derive the insurance premium under risk correlation under several risk scenarios. Under a first-order approximation, a quasi-linear relationship between the premium and the two major risk factors (the number of branches and the risk correlation coefficient) is determined. [ABSTRACT FROM AUTHOR]

Despite growing attention to cyber risks in research and practice, quantitative cyber risk assessments remain limited, mainly due to a lack of reliable data. This analysis leverages sparse historical data to quantify the financial impact of cyber incidents at the enterprise level. For this purpose, an operational risk database—which has not been previously used in cyber research—was examined to model and predict the likelihood, severity and time dependence of a company's cyber risk exposure. The proposed model can predict a negative time correlation, indicating that individual cyber exposure is increasing if no cyber loss has been reported in previous years, and vice versa. The results suggest that the probability of a cyber incident correlates with the subindustry, with the insurance sector being particularly exposed. The predicted financial losses from a cyber incident are less extreme than cited in recent investigations. The study confirms that cyber risks are heavy-tailed, jeopardising business operations and profitability. [ABSTRACT FROM AUTHOR]

Modeling cyber risks has been an important but challenging task in the domain of cyber security, which is mainly caused by the high dimensionality and heavy tails of risk patterns. Those obstacles have hindered the development of statistical modeling of the multivariate cyber risks. In this work, we propose a novel approach for modeling the multivariate cyber risks which relies on the deep learning and extreme value theory. The proposed model not only enjoys the high accurate point predictions via deep learning but also can provide the satisfactory high quantile predictions via extreme value theory. Both the simulation and empirical studies show that the proposed approach can model the multivariate cyber risks very well and provide satisfactory prediction performances. [ABSTRACT FROM AUTHOR]

Modeling cyber threats, such as the computer malicious software (malware) propagation dynamics in cyberspace, is an important research problem because models can deepen our understanding of dynamical cyber threats. In this paper, we study the statistical modeling of the macro-level evolution of dynamical cyber attacks. Specifically, we propose a Bayesian structural time series approach for modeling the computer malware propagation dynamics in cyberspace. Our model not only possesses the parsimony property (i.e. using few model parameters) but also can provide the predictive distribution of the dynamics by accommodating uncertainty. Our simulation study shows that the proposed model can fit and predict the computer malware propagation dynamics accurately, without requiring to know the information about the underlying attack-defense interaction mechanism and the underlying network topology. We use the model to study the propagation of two particular kinds of computer malware, namely the Conficker and Code Red worms, and show that our model has very satisfactory fitting and prediction accuracies. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]