Teoria das múltiplas vidas: uma abordagem por dependência

Abstract

One of the hypotheses commonly associated with actuarial calculations in life contingencies for groups is that the future lifetimes of each of its members are independent. Although assuming this hypothesis simplifies calculations, international actuarial literature presents evidence of dependence between future lifetimes for various groups, such as couples and twins, for example. Thus, this study aimed to analyze the effect of dependence between the future lifetimes of individuals within the same group on the pricing of annuities for couples. For this purpose, a database containing 2000 contracts was simulated, each referring to two policyholders, one male and one female. Three different mortality experiences were simulated for this database, resulting in three analyzed scenarios. After the simulations, non-parametric and parametric survival analyses were conducted, and based on the Likelihood Ratio Test and the Akaike Information Criterion, the Gompertz distribution was considered the most suitable to describe the future lifetime of policyholders in the three simulated scenarios. Based on this information, a dependency model was built for each scenario using copula functions selected by the Akaike Information Criterion. For Scenario 1, the Gumbel copula was chosen, while for Scenarios 2 and 3, the Clayton copula was selected. Through these models, whole life immediate annuities due for two lives under the last survivor status were calculated, considering and disregarding the dependency hypothesis, as well as the ratio between the two cases. The main results indicate that annuities calculated considering dependency are generally lower than when considering independence and, in several cases, are significantly different. Additionally, it was observed that each scenario achieved completely different results, indicating the specificity of each model and the assumption or non-assumption of the independesse premisse. Finally, the results highlighted the relevance of studying dependency in the pricing of products for couples.