Aggregate claim models with one-way and two-way dependence among individual claims

Abstract

Motivated by some real life correlations among insurance claims, we consider three aggregate claim models with dependence in this paper. Model one considers the dependence caused by a common index among indexed insurance benefits; model two takes into account the correlation arisen from common fixed costs; model three covers both types of dependence. Two random variables, Y 1 denoting a random index and Y 2 denoting a random cost, form the center part in the above three dependence models and detailed discussions are given on how the aggregate claims amount interacts with these sources of dependence. Theoretical results of these aggregate claim distributions are derived and algorithms for computational purposes are also provided. Some numerical results are presented for the compound Poisson case together with discussions and comparisons regarding the three dependence cases.