TITLE:
Modeling Cyber Loss Severity Using a Spliced Regression Distribution with Mixture Components
AUTHORS:
Meng Sun
KEYWORDS:
Cyber Risk, Data Breach, Spliced Regression Model, Finite Mixture Distribu-tion, Cluster Analysis, Expectation-Maximization Algorithm, Extreme Value Theory
JOURNAL NAME:
Open Journal of Statistics,
Vol.13 No.4,
July
11,
2023
ABSTRACT: Cyber losses in terms of
number of records breached under cyber incidents commonly feature a significant
portion of zeros, specific characteristics of mid-range losses and large
losses, which make it hard to model the whole range of the losses using a
standard loss distribution. We tackle this modeling problem by proposing a
three-component spliced regression model that can simultaneously model zeros,
moderate and large losses and consider heterogeneous effects in mixture
components. To apply our proposed model to Privacy Right Clearinghouse (PRC)
data breach chronology, we segment geographical groups using unsupervised
cluster analysis, and utilize a covariate-dependent probability to model zero
losses, finite mixture distributions for moderate body and an extreme value
distribution for large losses capturing the heavy-tailed nature of the loss
data. Parameters and coefficients are estimated using the Expectation-Maximization (EM) algorithm.
Combining with our frequency model (generalized linear mixed model) for data
breaches, aggregate loss distributions are investigated and applications on
cyber insurance pricing and risk management are discussed.