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Published online by Cambridge University Press: 22 April 2013
1. In the following Paper I propose to investigate formulas for use in the valuation of ordinary whole-term policies, endowment assurance policies, and limited-payment policies; with special reference to the modifications which these of formulas are subject, when the next premium Paper is due, not immediately, but at the end of some fractional portion of a year, and when the premiums are payable half-yearly or quarterly.
2. It may be well to point out that it is no part of my plan to deal with the more important questions of principle that arise in connection with a Life Office Valuation, such as:—What mortality table or rate of interest should be used, Whether the valuation ought to be a net premium or a gross premium valuation, How the effect of selection should be allowed for, or whether any allowance should be made for the special expenditure of the first year.
page 345 note * [Note.]—It will be convenient to use this phrase as an abbreviation for the “Institute of Actuaries' Text-Book. Part II. London, 1887.”
page 350 note * This figure is obtained as follows:—
page 352 note * This figure is obtained as follows:—
page 368 note * In a letter by Mr. King to the Journal of the Institute of Actuaries (xxviii. 160) he states that in arriving at those methods “the assumption is tacitly made that the premiums are really yearly premiums payable by instalments, so that those instalments for the current year, unpaid at the time of death, will fall to be deducted from the sum assured on settlement of the claim”; but they are here obtained without making any such assumption; and I think it clearly appears, from what is stated in articles 78–80, that they are sufficiently correct for practical use, even where the policies are subject to true half-yearly or quarterly premiums.
page 385 note * The following are the office premiums used in the construction of this table and Table Q, p. 393.
page 396 note * I have substituted the Symbols s and a for the s and a employed by Professor De Morgan, as these last have been already used in this Paper with a different signification.
page 397 note * See note at end of Paper.