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Published online by Cambridge University Press: 18 August 2016
A Net Premium Valuation is made when the sums assured and net premiums are valued at a given rate of interest and by a given table of mortality, and the net premiums are calculated at the same rate of interest and by the same table of mortality. Such a valuation leads to a reserve that starts with the net premium and ultimately reaches the sum assured for whole life assurances and endowment assurances; it cannot produce negative values unless the annuity value increases with the age, a case with which we are not concerned in this paper.
Page 63 note * I am grateful to M. E. Ogborn and W. P. Goodchild for help in the arithmetical work and to H. B. Smither for some tables additional to those published by him in J.I.A. Vol. LIX, p. 323.
Page 69 note * The objection to negative values is often stated in the form that a liability cannot be an asset. But a contract may be an asset at one moment and a liability at another. Circumstances can be imagined in which negative values are justifiable, e.g. the conditions might be that (1) an adequate level annual premium is charged, (2) the cost of risk plus initial expense exceeds the premium within a term of n years where n is small, usually unity, (3) the option of discontinuance is excluded or is known at the time of valuation not to have been exercised. The conditions are rare—No. (3) especially so—but indicate that a good general rule may be inapplicable to a particular case.
Page 93 note * If, by the means now discussed or otherwise, net premium valuations could be discontinued before the publication of new tables, the tabulations at low rates of interest of net premiums and of policy values would be unnecessary.
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