DOCSLIB.ORG

International Actuarial Notation 123

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
International Actuarial Notation 123 INTERNATIONAL ACTUARIAL NOTATION 123 INTERNATIONAL ACTUARIAL NOTATION ВУ F. S. PERRYMAN The Council of the Society announces that the revised International Actuarial N otation, particulars of which are given below, will Ье adopted in the Proceedings of the Society as from the present Number. The re­ vised Notation will also Ье used Ьу the Examination Committee for all examinations subsequent to those in Мау, i950. The revised Notation has been adopted Ьу the Society of Actuaries and also Ьу the Institute of Actuaries in England, the Faculty of Actuaries in Scotland and Ьу actuarial societies in various other foreign countries. Before giving an account of the circumstances leading up to the present revision and а complete account of the Notation it is desiraЫe to state here the principal changes which are now being introducd: " ( 1) Interest. In place of the symbol j (m) =the nominal rate of interest convertiЫe m times in а year when the effective rate is i, the symbol j(m) has been substituted; the former defini- tions of i (m) and [ as the effective rate of interest when interest is convertiЫe m times а year and momently respec­ tively have been abolished. "(2) Annuities-due. In place of the symbol а for an annuity under which the first payment is to Ье made at once the symbol а has been adopted. This adoption of the trema " as а symbol of acceleration has permitted the introduction of s for the ac­ cumulated amount of an annuity-due at the end of the term, for which no symbol previously existed. "(3) Mortality. The use of Q for the probaЬility of dying within а longer term than 1 year has been omitted. " (4) Compound symbols. The use of D in а compound symbol to indicate decreasing benefits has been introduced. "(5) Commutation columns. The old definition of Nx=Dx+i + Dx+ 2 + Dх+з etc. has been abolished in favour of Nx = Dx+ Dx+1 +Dx+2 etc. This renders the use of Nx and Nx for the latter series un­ necessary." The complete statement of the revised Notation and its history follows: 124 INTERNATIONAL ACTUARIAL NOTATION The existing international actuarial notation was founded on the ' Кеу to the Notatioп' given in the ]nstitute of Actuaries Text-Book, Part 11, Ltfe Con­ tingencies, Ьу George Кing, and is embodied in an exp\anatory statement adopted unaпimously Ьу the Second International Actuarial Congress held in London in Мау 1898 and printed оп рр. 618-40 of the Transactions of that Coпgress. At the Third lnterпatioпal Congress held iп Paris iri Juпe 1900 а further statemeпt Ьу Dr Sprague was submitted which rearranged the symbols iп different orders and grouped them оп differeпt principles but did поt iпtro­ duce апу chaпges iп the symbols themselves Ьеуопd two slight additioпs. This statemeпt is printed оп рр. 622-51 of the Transactions of that Congress. At the Eleventh Iпternational Congress held in Paris in Juпe 1937 an Iпternatioпal Committee was appoiпted to coпsider the question of пotation апd giveп the duty of submitting defiпite proposals to the пехt Congress. This Committee met iп Brussels iп July 1938 апd again in July 1939, апd certaiп chaп.,ges would have been propbsed for adoption at Lucerne iп l 940. 0·.ving to the war this could nQt Ье dопе, but in or.der not to lose the benefit of these changes for an indefinite · period the Iпstitute of Actuaries апd the Faculty of Actuaries have decided to adopt at а date to Ье mutually arranged those recommeпdatioпs which had received uпaпimous or substaпtial support at the meetiпgs of the Committee. As тапу studeпts апd members of the professioп have not ready access to the above-mentioned Transactions it has Ьееп thought desiraЬle to prepare апd issue the followiпg statemeпt of the Iпterпational Actuarial Notatioп after embodying iп it the chaпges arisiпg from the recommeпdations mentioned above. The geпeral principles оп which the system is based are as follows: То each fuпdamental symbolic letter are attached signs апd letters each haviпg its оwп sigпification. The lower space to the left is reserved for signs indicatiпg the coпditions relative to the duratioп of the operations and to their position with regard to time. The lower space to the right is r•:served for sigпs iпdicatiпg the conditioпs relative to ages and the order of succession of the everits. The upper space to the right is reserved for sigпs indicatiпg the periodicity of the events. The upper space to the left is free, and in it сап Ье placed signs corresponding to other notions. Iп what follows these two conventions are used: А letter enclosed in brackets, thus (х), denotes 'а persoп aged х'. А letter or numberenclosed iп а right angle, thus 7iJ or lsl, dt:пotes а term-certain ofyears. FUNDAMENTAL SYMBOLIC LETTERS Interest i = the effective rate of interest, пamely, the total interest earned on I in а year on the assumpti<;>n that the actual interest (if receivaЫe otherwise than yearly) is invested forthwith as it becomes due on the same terms as the original principal. INTERNATIONAL ACTUARIAL NOTATION 125 v = (1 +i)-1 = the present value of 1 due а year hence. d = 1 -v = the discount on 1 due а year hence. 3 = lo& ( 1 + i) = - lo& ( 1 -d) = the force of interest or the force of discount. Mortality ТаЬ!еS' l = number living. d = number dying. р = probaЬility of living. q = probaЬility of dying. µ = force of mortality. т = central death rate. а = present value of an annuity. S' = amount of an annuity. е = expectation of Iife. А = present value of an assurance. Е = present value of an endowment. Р} = prem~um per annum. Р generally refers to net premiums, ~т to special тт premшms. V = policy value. W = paid-up policy. The methods of using tl1e foregoing principal letters and their precise meaning when added to Ьу suffixes, etc., fo\1ow. Interest i<т> = т{(1+i) 1 fm_1} = the nomiпal 1·ate of interest, convertiЫe т times а year. ani = v + v2 + ... + v" = the valuc of an annuity-certain of 1 per annum for п years, tl1e payments being mad~ at the end of each year. 2 11 1 ап~ = 1 + v + v + ... + v - = the value of а similar annuity, the payments being made at the beginning of each year. 2 11 1 S'nJ = r + ( I + i) + ( r + i) + ... + ( 1 + i) - = the amount of an annuity-certain of 1 pcr annum for п years, the payments being made at the end of each year. sni = ( I + i) + ( I + i)2 + ., . + ( 1 +i)" = the amount of а similar annuity, the payments being made at the beginning of each year. The diaeresis or trema above the lette!"s а and s is used as а symbol of acceleration of payшcnts. Mortality ТаЫеs The ages of the lives involved are denoted Ьу letters placed as suffixes in the \o\ver space to the right. Thus: lж = the number of persons who attain age х according to the mortality tаЫе. dж = {" -!" ~ 1 = thc number of persons who die between ages х and х + r accordiг.g to the mortality tаЫе. Рж = the pl'ObaЬility that (х) will Iive 1 year. qж = the probaЬility that (х) will die within 1 year. 126 INTERNATIONAL ACTUARIAL NOTATION Р.х = - ~ ~; = the force of mortality at age х. тх = the central death-rate fo~ the year of age х to х + 1 = dx / f: lжн dt. ех = the curtate 'expectation of life' (or average after-lifetime) of (х). ln the following it is always to Ье understood (unless otherwise expressed) that the annual payment of an annuity is 1, that the sum assured in any case is 1, and that the symbols indicate the present values: ах= an annuity, first payment at the end of а year, to continue during the life of (х). iix = 1 +аж = an 'annuity-due' to continue during the life of (х), the first payment to Ье made at once. Ах = an assurance рауаЫе at the end of the year of death of (х). Note. ех =ах at rate of interest i =о. А letter or number at the lower left corner of the principal symbol denotes the number of years involved in the probability or benefit in question. Thus: пРх = the probaЬility that (х) wШ Iive п years. nqx == the probaЬility that (х) will die within п years. Note. When п = х it is customary to omit it, as shown on page 2, provided no amЬiguity is introduced. nEx == vnnPж = the valu'e of an endowment on (х) рауаЫе at the end of п years if (х) Ье then alive. If the letter or number comes before а perpendicular bar it shows that а period of deferment is meant. Thus: nlqx == the probaЬility that (х) will die in а year, deferred п years; that is, that he will die in the (п + 1 )th year. ~Jax == an annuity on (х) deferred п years; that is, that the first payment is to Ье made at the end of (п + х) years. nltax = an intercepted or deferred temporary annuity on (х) deferred п years and, after that, to run for t years. А letter or number in brackets at the upper right comer of the principal symbol shows the number of intervals into which the year is to Ье divided. Thus: а 1 ~ 1 = an annuity on (х) рауаЫе Ьу т instalments of i/m each throughout the year, the first payment being one of 1/т at the end of the first r/mth of а year.
Load more

Recommended publications
  • Supplementary Notes for Actuarial
    EDUCATION COMMITTEE OF THE SOCIETY OF ACTUARIES MLC STUDY NOTE SUPPLEMENTARY NOTES FOR ACTUARIAL MATHEMATICS FOR LIFE CONTINGENT RISKS VERSION 2.0 by Mary R. Hardy, PhD, FIA, FSA, CERA David C. M. Dickson, PhD, FFA, FIAA Howard R. Waters, DPhil, FIA, FFA Copyright 2011. Posted with permission of the authors. The Education and Examination Committee provides study notes to persons preparing for the examinations of the Society of Actuaries. They are intended to acquaint candidates with some of the theoretical and practical considerations involved in the various subjects. While varying opinions are presented where appropriate, limits on the length of the material and other considerations sometimes prevent the inclusion of all possible opinions. These study notes do not, however, represent any official opinion, interpretations or endorsement of the Society of Actuaries or its Education Committee. The Society is grateful to the authors for their contributions in preparing the study notes. Introduction This note is provided as an accompaniment to `Actuarial Mathematics for Life Contingent Risks' by Dickson, Hardy and Waters (2009, Cambridge University Press). Actuarial Mathematics for Life Contingent Risks (AMLCR) includes almost all of the material required to meet the learning objectives developed by the SOA for exam MLC for implementation in 2012. In this note we aim to provide the additional material required to meet the learning objectives in full. This note is designed to be read in conjunction with AMLCR, and we reference section and equation numbers from that text. We expect that this material will be integrated with the text formally in a second edition.
    [Show full text]
  • LIFE CONGINGENCY MODELS I Contents 1 Survival Models
    LIFE CONGINGENCY MODELS I VLADISLAV KARGIN Contents 1 Survival Models . 3 1.1 Survival function . 3 1.2 Expectation and survival function . 4 1.3 Actuarial notation . 8 1.4 Force of mortality . 13 1.5 Expectation of Life . 15 1.6 Future curtate lifetime. 18 1.7 Common analytical survival models . 20 2 Using Life Tables . 25 2.1 Life Tables. 25 2.2 Continuous Calculations Using Life Tables . 30 2.3 Select and ultimate tables . 35 3 Life Insurance . 38 3.1 Introduction . 38 3.2 Whole life insurance . 40 3.3 Term Life Insurance. 48 3.4 Deferred Life Insurance . 51 3.5 Pure Endowment Life Insurance . 55 3.6 Endowment Life Insurance. 56 3.7 Deferred Term Life Insurance . 58 3.8 Non-level payments paid at the end of the year . 59 3.9 Life insurance paid m times a year . 61 3.10 Level benefit insurance in the continuous case . 62 3.11 Calculating APV from life tibles. 64 3.12 Insurance for joint life and last survivor. 67 1 2 VLADISLAV KARGIN 4 Annuities . 72 4.1 Introduction . 72 4.2 Whole life annuities. 74 4.3 Annuities - Woolhouse approximation . 81 4.4 Annuities and UDD assumption . 84 5 Benefit Premiums . 86 5.1 Funding a liability. 86 5.2 Fully discrete benefit premiums: Pricing by equiva- lence principle . 87 5.3 Compensation for risk. 91 5.4 Premiums paid m times a year . 95 5.5 Benefit Premiums - Adjusting for Expenses . 96 VLADISLAV KARGIN 3 ~ SECTION 1 Survival Models The primary responsibility of the life insurance actuary is to maintain the solvency and profitability of the insurer.
    [Show full text]
  • O13 Actuarial Science
    o13 Actuarial Science Matthias Winkel1 University of Oxford MT 2003 1Departmental lecturer at the Department of Statistics, supported by Aon Ltd. and the Institute of Actuaries o13 Actuarial Science 16 lectures MT 2003 and 16 lectures HT 2004 Aims This course is supported by the Institute of Actuaries. It is designed to give the under- graduate mathematician an introduction to the financial and insurance worlds in which the practising actuary works. Students will cover the basic concepts of risk management models for mortality and sickness, and for discounted cash flows. In the final examina- tion, a student obtaining at least an upper second class mark on paper o13 can expect to gain exemption from the Institute of Actuaries' paper 102, which is a compulsory paper in their cycle of professional actuarial examinations. Synopsis Fundamental nature of actuarial work. Use of generalised cash flow model to describe financial transactions. Time value of money using the concepts of compound interest and discounting. Present values and the accumulated values of a stream of equal or unequal payments using specified rates of interest and the net present value at a real rate of interest, assuming a constant rate of inflation. Interest rates and discount rates in terms of different time periods. Compound interest functions, equation of value, loan repayment, project appraisal. Investment and risk characteristics of investments. Simple compound interest problems. Price and value of forward contracts. Term structure of interest rates, simple stochastic interest rate models. Single decrement model, present values and the accumulated values of a stream of payments taking into account the probability of the payments being made according to a single decrement model.
    [Show full text]
  • Fundamentals of Actuarial Mathematics Third Edition S
    Fundamentals of Actuarial Mathematics Third Edition S. David Promislow JWST504-fm JWST504-Promislow Printer: Yet to Come Trim: 244mm × 170mm October 13, 2014 7:17 ii JWST504-fm JWST504-Promislow Printer: Yet to Come Trim: 244mm × 170mm October 13, 2014 7:17 Fundamentals of Actuarial Mathematics i JWST504-fm JWST504-Promislow Printer: Yet to Come Trim: 244mm × 170mm October 13, 2014 7:17 ii JWST504-fm JWST504-Promislow Printer: Yet to Come Trim: 244mm × 170mm October 13, 2014 7:17 Fundamentals of Actuarial Mathematics Third Edition S. David Promislow York University, Toronto, Canada iii JWST504-fm JWST504-Promislow Printer: Yet to Come Trim: 244mm × 170mm October 13, 2014 7:17 This edition first published 2015 © 2015 John Wiley & Sons, Ltd Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to applyfor permission to reuse the copyright material in this book please see our website at www.wiley.com. The right of the author to be identified as the author of this work has been asserted in accordance withthe Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books.
    [Show full text]
  • Actuarialsymbol
    Actuarial symbols of life contingencies and financial mathematics∗ David Beauchemin [email protected] Vincent Goulet† [email protected] June 13, 2019 Abstract The package actuarialsymbol provides facilities to compose actuar- ial symbols of life contingencies and financial mathematics charac- terized by subscripts and superscripts on both sides of a principal symbol. The package also features commands to easily and con- sistently position precedence numbers above or below statuses in symbols for multiple lives contracts. Since actuarial notation can get quite involved, the package de- fines a number of shortcut macros to ease entry of the most common elements. Appendix A lists the commands to typeset a large selection of life contingencies symbols. Contents 1 Introduction2 2 For the impatient4 3 Package features4 3.1 Actuarial symbol . .4 3.2 Two-letter principal symbols . .6 3.3 Precedence numbers . .6 ∗This document corresponds to actuarialsymbol v1.1, dated 2019/06/13. †École d’actuariat, Université Laval 1 4 Shortcuts8 4.1 Basic symbols of life tables, insurance and annuities . .8 4.2 Symbols for premiums, reserves and paid-up insurance . 10 4.3 Auxiliary symbols . 10 4.4 Symbols for varying benefit insurance and annuities . 11 4.5 First, second and third precedence . 11 5 Package options 13 A Comprehensive life contingencies symbol list 14 B Implementation 27 B.1 Required packages . 27 B.2 Package options . 27 B.3 Actuarial symbol . 27 B.3.1 User level and parsing commands . 27 B.3.2 Symbol construction . 28 B.3.3 Shortcuts for basic symbols of life tables, insurance and annuities .
    [Show full text]
  • Actuarial Programming Methods
    ACTUARIAL PROGRAMMING METHODS by E. S. ROBERTSON, F.F.A. and A. D. WILKIE, M.A., F.F.A., F.I.A. [Submitted to the Faculty on 31st March 1969. A synopsis of the paper will be found on page 180.] 1. INTRODUCTION 1.1. For some years now actuaries have been using computers for data-processing work. This mainly involved problems of the mani- pulation of files of policies, the selection of the right action to take for a particular policy, and the printing of appropriate notices or summaries. Only incidentally did any actuarial calculation enter into the programs, and what did—valuation of policies or groups, calculations for surplus, calculations of valuation factors or recosting rates—was tackled either by conventional methods, or by the first convenient new method that came to hand. Also, however, com- puters began to be used for specifically actuarial problems—the calculation of tables of commutation columns and policy values, tables of premium rates, specific rates according to new methods. Again, either a conventional method was used, or whichever new method the actuary or programmer could conveniently devise. Each actuary or programmer had to tackle each problem afresh, since as yet no set of standard methods, especially suited for computer work, had been published. 1.2. Early computers required their programs to be written in a machine language, which was specific to the particular design of computer used, was not readily intelligible, and required a large number of individual simple instructions. Refinements of machine languages produced assembler languages directly related to machine language, though with mnemonic order codes and named locations; the current examples of these are ICL 1900 PLAN, and IBM/360 Assembler language.
    [Show full text]
  • Bs4a Actuarial Science I
    BS4a Actuarial Science I Matthias Winkel Department of Statistics University of Oxford MT 2017 SB4a Actuarial Science I 16 lectures MT 2017 Prerequisites A8 Probability is useful, but not essential. If you have not done A8 Probability, make sure that you are familiar with Prelims work on Probability. Synopsis Fundamental nature of actuarial work. Use of generalised cash-flow model to describe financial transactions. Time value of money using the concepts of compound interest and discounting. Interest rate models. Present values and the accumulated values of a stream of equal or unequal payments using specified rates of interest. Interest rates in terms of different time periods. Equation of value, rate of return of a cash-flow, existence criteria. Loan repayment schemes. Single decrement model. Present values and accumulated values of a stream of payments taking into account the probability of the payments being made according to a signle decrement model. Annuity functions and assurance functions for a single decrement model. Risk and premium calculation. Liabilities under a simple assurance contract or annuity contract. Premium reserves, death strain. Expenses and office premiums. Conventional and accumulation with-profits and unit- linked contracts, assurance and annuity functions involving two lives, valuing expected cash- flows in multiple decrement models, profit testing. Reading All of the following are available from the Faculty and Institute of Actuaries, 1st Floor, Park Central, 40/41 Park End Street, Oxford, OX1 1JD and https://www.actuaries.org.uk/shop. Subject CT1: Financial Mathematics Core reading. Institute & Faculty of Actuaries • Subject CT5: Contingencies Core Reading. Institute & Faculty of Actuaries. • J.
    [Show full text]
  • The Actuary Vol. 10, No. 3 the International Actuarial Notation
    Article from: The Actuary March 1976 – Volume 10, No. 3 PaEe Four THE ACTUARY March, 1976 Unruh THE INTERNATIONALACTUARIAL NOTATION (Continued from page 1) by Frank P. Di Pa010 is on a particular track, its future values should be based on that track. When it In the December 1972 issue of The Actuary, John Boermeester reviewed succinctly changes tracks, future values should the origin and history of the International Actuarial Notation, also known as the :!range with the new track. The expense Halo Notation. According to John Boermeester, the Halo Notation was invented by allowance calculated at issue should be David Jones who first used it in The YaZue of Annuities and Reversionary Payments based on the automatic track. Future published in Great Britain in 1844. With minor modifications, this notation was changes producin, u an increase in net officially adopted by the Institute of Actuaries in 1872 when it appeared in an Ap- premium should allow a related increase pendix to the Institute of Actuaries Life Tables. In 1898 the Halo Notation was in expense allowance. However, no de- adopted by the International Congress of Actuaries and, except for a number of crease in expense allowance should be minor changes which were made in 1954 during the XIV International Congress required if a change results in a de- of Madrid, it is still in use today. crease in net premium. The Halo Notation is basically an ideograph. The symbol representing the (2) For open policies that provide function is in the centre of the ideograph, while the symbols representing the para- contractually for the possibility of meters are shown, in accordance with well defined rules, as suffixed or prefixed sub- changes in benefits, premiums, or pre- (m) mium-paying period, but do not specify scripts and superscripts.
    [Show full text]
  • Tfa 32 (1969-1971) 42-71
    42 PROPOSALS FOR AN INTERNATIONAL ACTUARIAL PUBLICATION LANGUAGE AND ITS REPRESENTATION IN COMPUTER COMPATIBLE FORM by CARL BOEHM and GEORG REICHEL (Germany) in collaboration with A. BERTSCHE,H. HÄRLEN, M. HELBIG, G. HEUBECK(Germany) ; P. LEEPIN (Switzerland); G. LINDAUER,E. NEUBURGER(Germany); B. ROMER (Switzerland) ; A. SCHÜTZ(Germany) ; K.-H. WOLFF (Austria) [Excerpt from the Transactions of the 18th International Congress of Actuaries, Munich 1968, Volume II, pp. 815-836, Edition: Verlag Versicherungswirtschaft e.V., D75 Karlsruhe/West Germany 1968]. 1. INTRODUCTION 1.1. It has always been one of the concerns of the International Congress of Actuaries to standardize and codify the system of notation for actuarial terms. The efforts of the 2nd and 3rd Congresses (London 1898 and Paris 1900) and the work of the committee appointed by the 11th Congress (Paris 1937), which was completed at the 14th Congress (Madrid 1954), have led to a uniform system of notation for life insurance mathematics in educational establish- ments, in actuarial publications, in professional research, and in insurance companies. 1.2. Today pressures of various kinds are working towards a revision of this notation : (a) the need to extend, beyond the area of life assurance, the range of actuarial terms which have a standard definition— this therefore requires a real extension of the actuarial “ Vocabu- lary”; and (b) the necessity to model the notation in such a way that it can be easily and directly set up mechanically for data processing— this therefore demands more or less machine-linked representa- tions of the “ Vocabulary ”. The strongest pressure for this has certainly come in recent years with the use of electronic computers as printers and as program-controlled calculators.
    [Show full text]
  • Basic Life Insurance Mathematics
    Basic Life Insurance Mathematics Ragnar Norberg Version: September 2002 Contents 1 Introduction 5 1.1 Banking versus insurance . 5 1.2 Mortality . 7 1.3 Banking . 9 1.4 Insurance . 11 1.5 With-profit contracts: Surplus and bonus . 14 1.6 Unit-linked insurance . 16 1.7 Issues for further study . 17 2 Payment streams and interest 19 2.1 Basic definitions and relationships . 19 2.2 Application to loans . 25 3 Mortality 28 3.1 Aggregate mortality . 28 3.2 Some standard mortality laws . 33 3.3 Actuarial notation . 35 3.4 Select mortality . 37 4 Insurance of a single life 39 4.1 Some standard forms of insurance . 39 4.2 The principle of equivalence . 43 4.3 Prospective reserves . 45 4.4 Thiele's differential equation . 52 4.5 Probability distributions . 56 4.6 The stochastic process point of view . 57 5 Expenses 59 5.1 A single life insurance policy . 59 5.2 The general multi-state policy . 62 6 Multi-life insurances 63 6.1 Insurances depending on the number of survivors . 63 1 CONTENTS 2 7 Markov chains in life insurance 67 7.1 The insurance policy as a stochastic process . 67 7.2 The time-continuous Markov chain . 68 7.3 Applications . 73 7.4 Selection phenomena . 77 7.5 The standard multi-state contract . 79 7.6 Select mortality revisited . 86 7.7 Higher order moments of present values . 89 7.8 A Markov chain interest model . 94 7.8.1 The Markov model . 94 7.8.2 Differential equations for moments of present values .
    [Show full text]
  • Jia 75 (1949) 0121-0129
    121 INTERNATIONAL ACTUARIAL NOTATION THE existing international actuarial notation was founded on the ‘Key to the Notation’ given in the Institute of Actuaries Text-Book, Part II, Life Con- tingencies, by George King, and is embodied in an explanatory statement adopted unanimously by the Second International Actuarial Congress held in London in May 1898 and printed on pp. 618-40 of the Transactions of that Congress. At the Third International Congress held in Paris in June 1900 a further statement by Dr Sprague was submitted which rearranged the symbols in different orders and grouped them on different principles but did not intro- duce any changes in the symbols themselves beyond two slight additions. This statement is printed on pp. 622-51 of the Transactionsof that Congress. At the Eleventh International Congress held in Paris in June 1937 an International Committee was appointed to consider the question of notation and given the duty of submitting definite proposals to the next Congress. This Committee met in Brussels in July 1938 and again in July 1939, and certain changes would have been proposed for adoption at Lucerne in 1940. Owing to the war this could not be done, but in order not to lose the benefit of these changes for an indefinite period the Institute of Actuaries and the Faculty of Actuaries have decided to adopt those recommendations which had received unanimous or substantial support at the meetings of the Committee. The change is to take effect with Vol. LXXVIof the Journal and with the May 1950 examinations of the Institute of Actuaries.
    [Show full text]
  • An Actuarial Note on Actuarial Notation
    196 AN ACTUARIAL NOTE ON ACTUARIAL NOTATION JEFFREY T. LANGE “When Z use a word,” Humpty-Dumpty said, “it means just what Z choose it to mean - neither more nor less.” - Lewis Carroll One of the invariants in the Syllabus of Examinations of our Society has been the study of life insurance mathematics and the associated actu- arial notation. As a result probably every practicing actuary has, at one time or another, worked with this unique notation. Multiple indices appear both prefixed and suffixed to a symbol along with exponents resulting in a halo of characters about the basic symbol. Special print characters, e.g. horizontal bars, 1, O, '-, are used to modify both indices and basic symbols in order to alter the meaning of an expression. Sometimes the actuarial usage is quite different from ordinary practice; for example, exponents are not to be interpreted as exponents. The end result is that to the non-actuary the notation of the actuary may resemble the jottings of the astrologer or alchemist. The complexity of actuarial notation results in an unusual succinctness. An intricate insurance policy involving a number of benefit options and a complicated payment plan may be reduced to a single expression. Once a problem is translated into actuarial notation, it is frequently a relatively ele- mentary task to manipulate the symbols and solve the equations. Having learned the notation, even the student, equipped only with tables, pencil, and paper, can evaluate rather involved policy forms. The concise, compact form of the notation allows the experienced actuary to elegantly express complicated insurance schemes in a limited number of equations, which can be of great aid in obtaining a solution.
    [Show full text]