Measuring the impact of a dependence among insured life lengths

Actuaries usually compute multiple life premiums based on the unrealistic assumption of independence of the lifelengths of insured persons. Many clinical studies, however, have demonstrated dependence of the lifetimes of paired lives such as husband and wife. In this respect, the present article tries to give an answer to the following question: does this simplifying hypothesis constitute a real financial danger for the insurance company? The answer turns out to be affirmative: this dependence materially affects the values of annuities and insurances involving multiple lives. In order to quantify the impact of a possible dependence on the amount of premium charged for annuities, insurances and widow's pension, we resort here on the Fréchet bounds, Markov processes and some copula models. These techniques are applied to classical insurance contracts issued to married couples and illustrated on NIS data as well as on observations from Brussels city.