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On the valuation of life contingencies by means of tables of single and joint lives

1853; Cambridge University Press; Volume: 3; Issue: 3 Linguagem: Inglês

10.1017/s2046165800021092

2396-8222

Charles James Hargreave,

Insurance, Mortality, Demography, Risk Management

Let a 1 , a 2 . . a n be the reciprocals of the roots of the expression 1 − s 1 x + s 2 x 2 − . . ± s n −1 x n −1 ∓ s n x n , which call ϕx . We have then ϕx = (1 − a 1 x ) (1 − a 2 x ) . . . (1 − a n x ), from which the following series of values may be readily deduced, the Σ implying the sum of all the instances of the form placed under it, so that each expression is a symmetrical function of a 1 , a 2 . . a n . The sign is positive when p is even, and negative when p is odd. A single term of the p th expression contains p factors of the form a, and n–p factors of the form 1 – a ; and the expression itself is the sum of every term which can be so constructed.