EBiCop: Ensemble bivariate copulas for modeling multivariate cyber data breach risks

Modeling cyber data breach risks poses a formidable challenge, primarily due to the intricate multivariate dependencies within a backdrop of limited data. This study proposes a novel ensemble learning approach that effectively captures both the temporal and cross-sectional dependence inherent in cyber risks. The proposed approach is significantly different from those traditional ones that directly model the multivariate dependence among risks. Instead, our approach leverages bivariate copulas to generate predictive members to capture the multivariate dependence, and the resulting predictive distribution is calibrated by minimizing the distribution score. Furthermore, the proposed model is applied in insurance pricing, and the results show that it can lead to more profitable contracts. Through extensive simulations and analysis of real-world data, our findings reveal that the proposed model has satisfactory fitting and predictive performance and outperforms those in the literature.