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.
Highlights
Introduction and MotivationConsiderable attention is currently being devoted in insurance work to the management of life annuity portfolios and to the annuity product design, because of the growing importance of annuity benefits paid by private pension schemes and individual policies.In particular, the progressive shift in many countries from defined benefit to defined contribution pension schemes has increased the interest in life annuity products with a guaranteed periodic benefit
Special-rate life annuities are life annuity products whose single premium is based on a mortality assumption driven by the health status of the applicant
Cases 1.3 We assume that both enhanced annuities and impaired annuities are sold, and analyze the joint impact by assuming that n3 = n2/2
Summary
The main features of life annuity products are discussed in many life insurance and actuarial textbooks. Heterogeneity in mortality and risk classification constitute the natural frameworks in which the basic features of special-rate life annuities can be analyzed. Risk classification in life insurance and life annuities is addressed in many books and papers; a compact review, together with an extensive reference list, is provided by Haberman and Olivieri (2014). The impact of risk classification on the structure of life annuity portfolios is dealt with by Gatzert et al (2012), Hoermann and Russ (2008) and Olivieri and Pitacco (2016). Denuit and Frostig (2007) focusses on heterogeneity among lifetimes in the context of stochastic mortality according to the Lee-Carter model. The reader can refer to Pitacco (2019) for a literature review from an actuarial perspective, as well as for a discussion of models, which can be used to represent specific mortality rates accounting for observable risk factors. For a list of references the reader can refer to Pitacco and Tabakova (2020)
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