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Calculating devices and actuarial work

  • C. G. Lewin, J. V. Evans, K. J. Goodare and L. R. Packer


This paper is the report of a Research Group which has been examining developments in calculating devices, the effects on actuarial work and the future outlook.



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(1) King, G. (1887). Life Contingencies. Institute of Actuaries textbook of the principles of interest, life annuities and assurance, and their practical application. Part 2. London: C. & E. Layton.
(2) Spurgeon, E. F. (1922). Life Contingencies. Cambridge: C. & E. Layton.
(3) Moorhead, J. Unpublished chapter in proposed book: Our Yesterdays—How Actuaries Calculated.
(4) ‘Calculating Machines and Instruments’, Catalogue of the Collections in the Science Museum. Compiled by D. Baxandall and revised by Jane Pugh. Science Museum, 1975.
(5) Horsburgh, E. M. (Editor). (1914). Napier Tercentenary Celebration. Handbook of the exhibition of Napier relics and of books, instruments and devices for facilitating calculation. Edinburgh: Royal Society of Edinburgh.
(6) Hooper, W. J. A. (1950). ‘Punched card mechanisation and its application to insurance work’. Journal of the Chartered Insurance Institute. Volume 47. Pages 6173. (Also reprinted separately in 1952 by Powers-Samas Accounting Machines [Sales] Ltd.)
(7) Comrie, L. J. (1936). Speaker in the discussion of the paper: ‘Binary calculation’ by Phillips, E. William. J.I.A. 67, 208211.
(8) Vickers, T.Memory Lane’. Computer Bulletin. June 1986. Series III. Volume 2. Part 2. Page 40.
(9) Moreau, Rene. (1984). The computer comes of age: The people, the hardware, and the software. Massachusetts Institute of Technology Press.
(10) BPA (Technology and Management) Ltd. (1986). ‘Electronics: an industry in transition’. London: Financial Times Business Information.
(11) English Life Table. (1864). Tables of lifetimes, annuities, and premiums; with an introduction by William Farr, M.D., F.R.S., D.C.L. Published by authority of the Registrar-General of Births, Deaths, and Marriages in England. London: Longman & Co.
(12) Hannyngton, J. C. Major-General (1866). ‘On the adaptation of assurance formulae to the arithmometer of M. Thomas.’ Correspondence, April 1865. J.I.A. 12, 184.
(13) Hannyngton, J. C. Major-General (1872). ‘On the use of M. Thomas de Colmar's Arithmometer in actuarial and other computations’. J.I.A. 16, 244253.
(14) Hardy, R. P. (1873) Valuation tables, based upon the Institute of Actuaries mortality experience (HM) table, at 3, 3½, 4 and 4½ per cent with other useful tables. Calculated by the arithmometer invented by Thomas, M. (de Colmar). London: C. & E. Layton.
(15) Chisholm, D. (1852). ‘On a new method of constructing a table of the probabilities of survivorship between two lives for every combination of ages, and also a table of the present value of survivorship assurances of £1 on (x) against (y)’. J.I.A. 2, 305332.
(16) Sang, E. Life assurance and annuity tables, with a copious collection of rules and examples. Two volumes. Edinburgh: Edward Sang, 1841 (Volume 1); London: Edward Sang, 1859 (Volume 2).
(17) Henry, J. (1869). ‘Memoir on instrument for furnishing the D numbers, to four figures each, in two joint life annuity tables, on any basis’. J.I.A. 14, 212226.
(18) Laundy, S. L. (1861). ‘On a method of using the “Table of quarter squares”.’ Correspondence, March 1860. J.I.A. 9, 112115.
(19) Oakes, Lieut.-Col. Wm. H. (1863). ‘A method of multiplication which may be practised mentally’. J.I.A. 10, 326327.
(20) Crelle, A. L. (1820) Rechentafeln welche alles multipliciren und dividiren mit Zahlen unter tausend ganz ersparen, bei grosseren Zahlen aber die Rechnung erleichtern und sicherer machen. Berlin: Georg Reimer. (First English edition: Dr Crelle, A. L.'s Calculating tables, revised by Dr. C. Bremiker. London: David Nutt, 1897.)
(21) Cotsworth's Direct Calculator (1894). London: Crosby Lockwood & Son.
(22) Davie, J. & Scrimgeour, D. A. B. (1930). ‘A method of using mechanical sorting and tabulating for the preparation and issue of bonus intimations’. T.F.A. 12, 249259.
(23) Barnard, W. T. L. (1965). ‘Some changes in actuarial methods arising from the use of a small computer in a medium-sized office’. J.I.A. 91, 108129.
(24) Davidson, A. R. (1930). Speaker in the discussion of the paper by Davie J. and Scrimgeour D. A. B. ‘A method of using mechanical sorting and tabulating for the preparation and issue of bonus intimations’. T.F.A. 12, 265266.
(25) Phillips, E. W. (1936). ‘Binary calculation’. J.I.A. 67, 187203.
(26) Churchhouse, R. F. (1980). ‘Computer arithmetic and the failure of the Associative Law’. Bulletin of the Institute of Mathematics and its Applications 16, No. 10, 210214.
(27) Redington, F. M. (1969). ‘An Exploration into Patterns of Mortality’. J.I.A. 95, 278.
(28) Benjamin, S. (1966). ‘Putting Computers on to Actuarial Work’. J.I.A. 92, 134171.
(29) Michaelson, R. L. (1953). ‘Large Scale Electronic Digital Computing Machines’. J.I.A. 79, 274297.
(30) Baker, A. C. (1955). ‘Ordinary Life Office Organisation using a large-scale Electronic Computer’. J.I.A. 81, 203237.
(31) Jecks, R. G. (1962) ‘Administration of Group Life and Pensions Business by Computer’. J.I.A. 88, 133160.
(32) Gray, P. (1873). ‘On the Arithmometer of M. Thomas (de Colmar) and its application to the Construction of Life Contingency Tables’. J.I.A. 17, 249266, J.I.A. 18, 20-32 and 123-132.
(33) Carment, D. (1880) ‘On the Application of the Arithmometer to the Construction of Tables of the Values of Endowment Assurance Policies’. J.I.A. 22, 368380.
(34) Fackler, D. P. (1902). ‘Regarding the Mortality Investigation, instituted by the Actuarial Society of America and now in progress’. (Contains photographs of early punched-card equipment.) J.I.A. 37, 115.
(35) D'Ocagne, M. (1905). ‘The Simplification of Calculations by Mechanical and Graphical Processes’. Book Review by ‘W.R.S.’. J.I.A. 39, 377379.
(36) Plummer, H. C. (1912). ‘On Aids to calculation, with special reference to some recently published Tables’. J.I.A. 46, 193197.
(37) Scrimoeour, D. A. B. (1950). ‘The use of ’Powers” cards for the calculation of repayment schedules under annuities-certain’. T.F.A. 20, 7882.
(38) Glaisher, J. W. L. (1980). ‘The Method of Quarter Squares’. J.I.A. 28, 227235.
(39) Bennett, M. C., Berry, P. K., Brown, G. A., Farrington, G. W. & Hey, G. B. (1974). ‘An Approach to the Use of Computers in Actuarial Work’. J.I.A. 101, 299331.
(40) Burrough, Sheila M. & Hey, G. B. (1981). ‘Table Making and Interpolation’. J.I.A. 108, 265280.
(41) Recce, M. & Treleavan, P. ‘Computing from the Brain’. New Scientist, 26 May 1988, pp. 6164.
(42) Williams, M. R.Difference Engines’. The Computer Journal, February 1976, pp. 8288.
(43) Cendrowska, J. & Bramer, M. (1984). ‘Inside an Expert System: A Rational Reconstruction of the MYCIN Consultation System’. From ‘Artificial Intelligence’; by Tim O'Shea and Marc Eisenstadt, pp. 453497.
(44) Encyclopedia Britannica, 11th Edition. 1910-11. Articles on ‘Calculating Machines’ and ‘Table, Mathematical’.
(45) Ball, W. W. Rouse (1917). ‘Mathematical Recreations and Essays’, London (seventh edition). Chapter XII deals with arithmetical calculating machines.
(46) Lucas, M. E. (1893). ‘Recreations Mathematiques’. Paris. Volume III contains a chapter entitled “Les Machines a calculer”. Pages 5986.
(47) Smith, D. E. ‘History of Mathematics’, Dover reprint, pp. 202206 of volume II deal with calculating devices.
(48) Four papers by King, George containing voluminous calculations: ‘On the Mortality among Assured Lives and the Requisite Reserves of Life Offices. Part I, Statistical.’ J.I.A. 19, 381.
On the Mortality among Assured Lives and the Requisite Reserves of Life Offices. Part II, Financial.’ J.I.A. 20, 233.
On the comparative Reserves of Life Assurance Companies according to various Tables of Mortality, at Various Rates of Interest.’ J.I.A. 37, 453.
On the Valuation in Groups of Whole-Life Policies by Select Mortality Tables.’ J.I.A. 40, 1.
(49) Beard, R. E. (1943). ‘The construction of a small-scale differential analyser and its application to the calculation of actuarial functions.’ J.I.A. 71, 193211.

Calculating devices and actuarial work

  • C. G. Lewin, J. V. Evans, K. J. Goodare and L. R. Packer


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