Solvency requirement in a unisex mortality model

Following the EU Gender Directive, that obliges insurance companies to charge the same premium to policyholders of different genders, we address the issue of calculating solvency capital requirements (SCRs) for pure endowments and annuities issued to mixed portfolios. The main theoretical result is that, if the unisex fairness principle is adopted for the unisex premium, the SCR of the mixed portfolio calculated at issuing time assuming unisex survivorship is greater than the sum of the SCRs of the gender based subportfolios. Numerical results show that for pure endowments the gap between the two is negligible, but for lifetime annuity the gap can be as high as 3-4%. We also analyze some conservative pricing procedures that deviate from the unisex fairness principle, and find that they lead to SCRs that are lower than the sum of the gender based SCRs, because the policyholders are overcharged at issuing time.