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A life annuity is an annuity, or series of payments at fixed intervals, paid while the purchaser (or annuitant) is alive. A life annuity is an insurance product typically sold or issued by life insurance companies. Life annuities may be sold in exchange for the immediate payment of a lump sum (single-payment annuity) or a series of regular payments (flexible payment annuity), prior to the onset of the annuity. The payment stream from the issuer to the annuitant has an unknown duration based principally upon the date of death of the annuitant. At this point the contract will terminate and the remainder of the fund accumulated is forfeited unless there are other annuitants or beneficiaries in the contract. Thus a life annuity is a form of longevity insurance, where the uncertainty of an individual's lifespan is transferred from the individual to the insurer, which reduces its own uncertainty by pooling many clients. Annuities can be purchased to provide an income during retirement, or originate from a ''structured settlement'' of a personal injury lawsuit. ==History== The instrument's evolution has been long and continues as part of actuarial science.〔(【引用サイトリンク】title=Laboratory of Actuarial Mathematics )〕 Ulpian is credited with generating an actuarial life annuity table between AD 211 and 222. Medieval German and Dutch cities and monasteries raised money by the sale of life annuities, and it was recognized that pricing them was difficult.〔J. Franklin, ''The Science of Conjecture: Evidence and Probability Before Pascal'' (Baltimore: Johns Hopkins University Press, 2001), 269-272.〕 The early practice for selling this instrument did not consider the age of the nominee, thereby raising interesting concerns.〔"(From Commercial Arithmetic to Life Annuities: The Early History of Financial Economics, 1478-1776 )" Goeffrey Poitras, Simon Fraser University〕 These concerns got the attention of several prominent mathematicians〔(Seminar Series on Quantitative Finance ) The Fields Institute〕 over the years, such as Huygens, Bernoulli, de Moivre and others:〔 even Gauss and Laplace had an interest in matters pertaining to this instrument.〔Stephen Hawking ''God Created the Integers: The Mathematical Breakthroughs That Changed History'', Running Press, 2005 ISBN 0-7624-1922-9〕 It seems that Johan de Witt was the first writer to compute the value of a life annuity as the sum of expected discounted future payments, while Halley used the first mortality table drawn from experience for that calculation. Meanwhile, the Paris Hôtel-Dieu offered some fairly priced annuities that roughly fit the Deparcieux table discounted at 5%.〔Pierre-Charles Pradier, « Les bénéfices terrestres de la charité. Les rentes viagères des Hôpitaux parisiens 1660-1690 » Histoire & mesure (décembre 2011, à paraître).〕 Continuing practice is an everyday occurrence with well-known theory founded on robust mathematics, as witnessed by the hundreds of millions worldwide who receive regular remuneration via pension or the like. The modern approach to resolving the difficult problems related to a larger scope for this instrument applies many advanced mathematical approaches, such as stochastic methods, game theory, and other tools of financial mathematics. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Life annuity」の詳細全文を読む スポンサード リンク
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