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Risks 2016, 4(4), 39;

Frailty and Risk Classification for Life Annuity Portfolios

Department of Economics, University of Parma, Via J.F. Kennedy 6, 43125 Parma, Italy
DEAMS ‘B. de Finetti’, University of Trieste, Via dell’Università 1, 34100 Trieste, Italy
Author to whom correspondence should be addressed.
Academic Editor: Mogens Steffensen
Received: 15 September 2016 / Revised: 14 October 2016 / Accepted: 17 October 2016 / Published: 26 October 2016
(This article belongs to the Special Issue Designing Post-Retirement Benefits in a Demanding Scenario)
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Life annuities are attractive mainly for healthy people. In order to expand their business, in recent years, some insurers have started offering higher annuity rates to those whose health conditions are critical. Life annuity portfolios are then supposed to become larger and more heterogeneous. With respect to the insurer’s risk profile, there is a trade-off between portfolio size and heterogeneity that we intend to investigate. In performing this, there is a second and possibly more important issue that we address. In actuarial practice, the different mortality levels of the several risk classes are obtained by applying adjustment coefficients to population mortality rates. Such a choice is not supported by a rigorous model. On the other hand, the heterogeneity of a population with respect to mortality can formally be described with a frailty model. We suggest adopting a frailty model for risk classification. We identify risk groups (or classes) within the population by assigning specific ranges of values to the frailty within each group. The different levels of mortality of the various groups are based on the conditional probability distributions of the frailty. Annuity rates for each class then can be easily justified, and a comprehensive investigation of insurer’s liabilities can be performed. View Full-Text
Keywords: voluntary annuities; underwritten annuities; heterogeneity; standard risk; substandard risk; preferred risk; issue-select mortality rates voluntary annuities; underwritten annuities; heterogeneity; standard risk; substandard risk; preferred risk; issue-select mortality rates

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Olivieri, A.; Pitacco, E. Frailty and Risk Classification for Life Annuity Portfolios. Risks 2016, 4, 39.

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