Cybersecurity Insurance Modeling Using Archimedean Copulas

Abstract

While technology has brought many benefits, it has also created challenges, including a rise in cyber-crime. One major issue is the spread of malware, such as viruses, which can threaten personal, business, and national security. This can be countered by purchasing cybersecurity insurance. To accommodate the increasing demand, it is necessary to provide the adequate method to measure the risks and estimate the premium charge. In this paper, the modeling of the infection and recovery process of an electrical device that is represented as a node in a network system is discussed. The model that is discussed is a non-Markov model with dependence between cybersecurity risks, which is modeled by the Archimedean copula function, namely Clayton, Frank, and Gumbel. Furthermore, the premium charge is estimated using standard deviation and the exponential utility principle. Based on the simulation, it can be concluded that a node connected with several nodes is more likely to be infected than a node connected with fewer number of nodes. Modeling infection times between nodes using the Gumbel copula function generates higher premiums than other copula functions, therefore it is better to use the Gumbel copula function for modeling cybersecurity insurance in the first contract period because insured companies tend to be more interested in extending the contract if the premium charge of the subsequent year is less than or equal to the rate of the previous year. In addition, changes in parameter of times-to-infections from neighbors does not cause a significant difference in expected number of infections, expected losses, and premium charge.