Actuariat et Risque Contemporains
Time : 11h00
Date : 02th  October 2025

Renata ALCOFODARO (Federal University of Pernambuco & Chaire ACTIONS) “Risk model with dependent frequency and severity for Liability and Housing Insurance”

Abstract: A common assumption in classical risk theory is the independence between claim frequency and severity. However, this often fails in practice, especially when subtle or nonlinear dependencies are present. This study analyzes a real-world dataset comprising 15,665 claims from housing and liability insurance contracts, recorded between 01/01/2015 and 31/12/2019, provided by an anonymous insurer. Unlike most literature focused on automobile insurance, our data allow us to explore dependence in less-studied lines of business, which pose unique challenges. We
investigate the presence and nature of dependence between frequency and severity, and how this relationship evolves over time and across insurance types. Our approach combines parametric and nonparametric methods: we fit Poisson-Inverse Gaussian, Negative Binomial, Weibull, and Log-Normal distributions to the marginals, and apply copula-based techniques to assess joint behavior. Using pseudo-observations, we estimate empirical copulas, visualize joint densities, and perform statistical tests of independence and equality (KcopTest), which reveal a structural break in housing insurance in 2016. Results indicate strong positive dependence in liability insurance. In housing insurance, we find near-independence in most years, but a weak and significant negative dependence in 2016. Finally, GAMLSS models confirm diverging patterns: in liability insurance, severity increases with frequency; in housing insurance, it decreases, in contrast to findings by Garrido (2016). We discuss implications for pricing, reserving, and solvency assessment under dependence.

References.
[1] Garrido, J., Genest, C., and Schulz, J. (2016). Generalized linear models for dependent frequency and severity of insurance claims Insurance: Mathematics and Economics 70, 205-215.

Organisateurs : Hillairet Caroline, Olivier Lopez