C. Bolancé Losilla, R. Vernic, A. Badea
This work introduces a novel bivariate composite distribution that merges the bivariate lognormal distribution for modeling lower costs with the bivariate Pareto distribution for capturing extreme costs. We establish key mathematical properties, including continuity and differentiability, and propose an estimation method based on partial likelihood maximization, considering both constrained and unconstrained continuity cases. A simulation study is conducted to assess the finite sample performance of the proposed estimator. Finally, we apply our model to bivariate car insurance cost data, illustrating its practical utility in risk assessment. Specifically, we demonstrate how the model can be used to estimate risk using Value-at-Risk and Tail Value-at-Risk measures for both total and conditional losses. These findings highlight the model’s effectiveness in handling heavy-tailed insurance claims and its potential applications in actuarial science and financial risk management.
Keywords: dependence, composite distributions, bivariate lognormal, bivariate Pareto, extremes
Scheduled
AR1 Risk analysis I
June 12, 2025 11:30 AM
MR 1