Life Annuities. Products, Guarantees, Basic Actuarial Models.

90 Pages Posted: 19 Dec 2016 Last revised: 22 Mar 2017

See all articles by Ermanno Pitacco

Ermanno Pitacco

University of Trieste - Dipartimento di Scienze Economiche, Aziendali, Matematiche e Statistiche B. de Finetti

Date Written: March 2017


These Lecture Notes aim at introducing technical and financial aspects of the life annuity products, with a special emphasis on the actuarial valuation of life annuity benefits. The text has been planned assuming as target readers: - advanced undergraduate and graduate students in Economics, Business and Finance; - advanced undergraduate students in Mathematics and Statistics, possibly aiming at attending, after graduation, actuarial courses at a master level; - professionals and technicians operating in insurance and pension areas, whose job may regard investments, risk analysis, financial reporting, and so on, hence implying communication with actuarial professionals and managers.

Given the assumed target, the use of complex mathematical tools has been avoided.

We assume that the reader has attended courses providing basic notions of Financial Mathematics (interest rates, compound interest, present values, accumulations, annuities, etc.) and Probability (probability distributions, conditional probabilities, expected value, variance, etc). As mentioned, Mathematics has been kept at a rather low level. Indeed, all topics are presented in a “discrete” framework, thus not requiring analytical tools like differentials, integrals, etc.

The Lecture Notes are organized as follows. Guarantees and options in life contingency products, and in life annuities in particular, are sketched in Chap. 1. In Chap. 2 the basic actuarial aspects are introduced with reference to conventional life annuity products, starting from expected present value definitions, then moving to premium and reserve calculations.

A more general framework is proposed in Chap. 3, in order to introduce a wide range of life annuity products. The guarantee structure implied by various products is analyzed in Chap. 4, while Chap. 5 focusses on the time profile of the annuity benefits.

Options and riders which can be added to life annuity products are dealt with in Chap. 6, while Chap. 7 focusses on annuity rates adopted to determine the annuity premiums. Cross-subsidy mechanisms working in life annuity portfolios are addressed in Chap. 8, where special attention is placed on “tontine” schemes.

Strategies, which can be adopted to get the post-retirement income and, to some extent, can constitute alternatives to the immediate full annuitization of resources available at retirement, are described in Chap. 9.

Long-term care insurance (LTCI) is briefly addressed in Chap. 10, with a special focus on life annuity benefits combined with LTCI benefits. Finally, Chap. 11 concludes with suggestions for further reading.

Keywords: post-retirement income, annuity benefits, living benefits

JEL Classification: G22

Suggested Citation

Pitacco, Ermanno, Life Annuities. Products, Guarantees, Basic Actuarial Models. (March 2017). Available at SSRN: or

Ermanno Pitacco (Contact Author)

University of Trieste - Dipartimento di Scienze Economiche, Aziendali, Matematiche e Statistiche B. de Finetti

Piazzale Europa 1
Trieste, Trieste 34100

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