Excess of age transfer policy for life annuities under longevity risk

In order to mitigate a life annuity provider’s (insurer’s) longevity risk exposure, we propose a general longevity risk transfer policy between the insurer and a reinsurer. The reinsurance premium is calculated according to the expected premium principle. Under an expected utility maximization framework, we apply the variational method to derive the necessary and sufficient condition for the optimal longevity risk transfer policy. We find that the optimal strategy takes the form of excess of age policy, which means that the insurer is only liable for the benefit payment up to the optimal deductible age, and the remaining benefit payment is covered by the reinsurer. Furthermore, we assess the viability of the reinsurer underwriting the optimal longevity risk transfer policy. Numerical examples show that the optimal longevity risk transfer policy can effectively improve the insurer’s relative gains and reduce the insurer’s longevity risk exposure.