The Modeling of Cyber Risk Insurance by Hawkes Processes With Loss Covariate

Abstract

The complexity and dynamic nature of cyber risks pose considerable challenges to risk management. From an actuarial perspective, we propose an advanced aggregate loss process using a variant of the Hawkes process as its frequency model. The refined Hawkes process first considers the impact of loss magnitude on the frequency of risk occurrences by integrating the loss covariate into the conditional intensity function. Second, we employ a more flexible kernel function in place of the classical exponential case. By incorporating the concept of age-dependent population structure, we calculate the probabilistic properties (mean, variance) for the proposed aggregate loss process. Furthermore, numerical simulations for cyber insurance pricing are conducted based on two pricing principles. Finally, we verify the feasibility of the proposed model based on a publicly available cyber breach data set. Considering the complex and dynamic nature of cyber risks, the efficiency of the proposed model is still limited by some factors, such as the authenticity and accuracy of the data. These are worthy of further consideration in future studies.