A study on life insurance premiums under asymmetric dependence using Canadian insurance data

This study evaluates the impact of symmetric and asymmetric dependence on premium calculations for various annuity and life insurance products across different age groups. Initially, we determined the marginal survival probabilities for individual lifetimes at specific ages using the Gompertz mortality model. Subsequently, joint survival probabilities were derived, considering independent and dependent future lifetimes for individuals within a group. The dependency structure was examined using Archimedean copulas for symmetric models and Khoudraji copulas for asymmetric models, which are widely referenced in the literature. In addition, actuarial calculations were conducted using real data on dependent lifetimes sourced from a Canadian insurance company. The data set is divided into three different populations based on age differences between married couples: the entire population without considering age differences, the population where males are older, and the population where females are older. The symmetric and asymmetric dependence structures of these populations were determined using an asymmetry test. The best-fitting models were identified using maximum likelihood estimation and goodness-of-fit tests. Finally, actuarial calculations were performed on the data set. Our findings showed that there were no significant differences between symmetric and asymmetric premium calculations for the whole population. However, when the population is disaggregated by age, the asymmetry becomes evident in the data structures, which increases the differences in the premium calculations. For example, the Kho-Fr model selected for the population of older female exhibiting asymmetric dependency was generally found to produce higher premiums than the Gumbel model. These findings reveal the importance of determining the dependency structure and working with age-based sub-populations rather than treating the whole population as a homogenous structure in model selection.