Special-Rate Life Annuities : Analysis of Portfolio Risk Profiles

Standard life annuities are attractive mainly for healthy people. Premium rates are consequently kept high. Hence, a large portion of potential annuitants are out of reach of insurers. In order to expand their business, some insurers have started offering better annuity rates to people whose health conditions are worse than those of likely buyers of standard life annuities. Special-rate life annuity (or underwritten life annuity) products have then been designed and launched. The underwriting step will result in assigning the applicant to a specific rating class. Hence, the special-rate line of business (LoB) is arranged in a set of sub-portfolios, which, together with the standard life annuity sub-portfolio, constitutes the life annuity LoB. Premium rates must be determined according to the (assumed) lifetime probability distribution of individuals belonging to the various sub-portfolios. 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 follows, inside each sub-portfolio of special-rate annuities. The variance of each life annuity payout of course impacts on the overall risk profile of the life annuity portfolio. On the one hand a higher premium income can be expected, on the other a higher variability of the total portfolio payout must be faced, because of both the larger size and the specific high variability of the payouts related to special-rate annuities. What about the “balance”?The present research aims at analyzing the impact of extending the life annuity LoB by including 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. Although results we have obtained clearly depend on assumptions (notably, regarding the lifetime distributions), interesting achievements witness the possibility of extending the 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 LoB risk profile