Special-Rate Life Annuities: Analysis of Portfolio Risk Profiles

Abstract

Special-rate life annuities are life annuity products whose single premium is based on a mortality assumption driven (at least to some extent) by the health status of the applicant. The health status is ascertained via an appropriate underwriting step (which explains the alternative expression “underwritten life annuities”). Better annuity rates are then applied in presence of poor health conditions. The worse the health conditions, the smaller the modal age at death (as well as the expected lifetime), but the higher the variance of the lifetime distribution. The latter aspect is due to significant data scarcity as well as to the mix of possible pathologies leading to each specific rating class. A higher degree of (partially unobservable) heterogeneity inside each sub-portfolio of special-rate annuities follows, and this results in a higher variability of the total portfolio payout. The present research aims at analyzing the impact of extending the life annuity portfolio by selling special-rate life annuities. Numerical evaluations have been performed by adopting a deterministic approach as well as a stochastic one, according to diverse assumptions concerning both lifetime distributions and portfolio structure and size. Our achievements witness the possibility of extending the annuity business without taking huge amounts of risk. Hence, the risk management objective “enhancing the company market share” can be pursued without significant worsening of the annuity portfolio risk profile.