Construct · 3 fields · 4 citations

Where does annuity collide?

One name. Different field. Different construct. One map.

● jingle · one word, three constructs Nearest construct by meaningmortalitycompare the meanings
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Every construct on the map is compared with every other by the meaning of its definitions, and the closest one is surfaced here. The nearest construct to annuity is mortality.

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annuity3 CONSTRUCTSAnnuity-certainKELLISON · FIXED STREAMLife annuityHALLEY · LIFE ANNUITYAnnuity puzzleYAARI · ANNUITY PUZZLE

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1693Life annuity1965Annuity puzzle2009Annuity-certain
2026

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Financial mathematics

A fixed stream of equal payments

In the mathematics of interest an annuity is any series of equal payments made at fixed, regular intervals, valued by discounting each payment back to the present at a stated interest rate. Kellison's The Theory of Interest (2009) sets out the standard formulas for the present and accumulated value of such a series, distinguishing an annuity-immediate, paid at the end of each period, from an annuity-due, paid at the start. Here the number of payments is fixed and known, so the same identity prices a mortgage, a bond's coupons, or a car loan. This referent is a deterministic valuation formula for a known series, not a payout that stops at death, not a household's puzzling reluctance to buy longevity insurance, and not a legal right charged on a person.[1]

Unit
One equal periodic payment in a fixed-length series, valued at a stated interest rate
Recovery means
Not applicable
Measured by
Computed as a present or accumulated value using the standard annuity-immediate or annuity-due formula

Actuarial science

A payment stream contingent on survival

In actuarial science a life annuity is a series of payments that continues only while a named person is alive, so the number of payments is not fixed but a random quantity governed by a mortality table. Valuing it means weighting each future payment by the probability that the annuitant survives to receive it and then discounting for interest, which yields an expected present value rather than a certain one. Halley's 1693 study of the Breslau bills of mortality built the first such table and used it to compute, as its title puts it, the price of annuities upon lives. This referent is a mortality-weighted expectation over an uncertain lifetime, distinct from the fixed-term formula of financial mathematics, from the economic question of why people avoid annuities, and from the lawyer's annuity as a property right.[2]

Unit
One survival-contingent payment, weighted by the chance the annuitant is alive to receive it
Recovery means
Not applicable
Measured by
Priced as an expected present value from a life table and an interest rate, using life-contingency functions

Economics

A good people should buy but mostly do not

In economics the annuity is a good that a rational saver is predicted to want and yet, in practice, mostly declines to buy. Yaari's 1965 model of a consumer with an uncertain lifetime showed that, absent a motive to leave a bequest, such a person should convert nearly all wealth into life annuities, because an annuity pays a survival premium that ordinary saving cannot match. The wide gap between that prediction and the thin market for voluntary annuities is what Davidoff, Brown, and Diamond's 2005 Annuities and Individual Welfare analysed as the annuity puzzle. This referent is a welfare claim and a demand anomaly about a financial product, not the payment-series formula of financial mathematics, not the actuarial pricing of a life-contingent stream, and not a legal right to fixed sums.[3][4]

Unit
A unit of wealth converted into guaranteed lifetime income, judged by its welfare gain
Recovery means
Not applicable
Measured by
Assessed by annuity-equivalent wealth in a life-cycle model and by observed take-up in annuity markets

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Nearby collisions

discount3 fields · 4 citationsjingle · one word, three constructsrent2 fields · 3 citationsjingle · one word, two constructsyield4 fields · 4 citationsjingle · one word, four constructs

References

  1. Kellison, S. G. (2009). The theory of interest (3rd ed.). McGraw-Hill/Irwin.
  2. Halley, E. (1693). An estimate of the degrees of the mortality of mankind, drawn from curious tables of the births and funerals at the city of Breslaw. Philosophical Transactions of the Royal Society of London, 17(196), 596–610. https://doi.org/10.1098/rstl.1693.0007
  3. Yaari, M. E. (1965). Uncertain lifetime, life insurance, and the theory of the consumer. The Review of Economic Studies, 32(2), 137–150. https://doi.org/10.2307/2296058
  4. Davidoff, T., Brown, J. R., & Diamond, P. A. (2005). Annuities and individual welfare. American Economic Review, 95(5), 1573–1590. https://doi.org/10.1257/000282805775014281

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