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The Actuary Vol. 10, No. 3 the International Actuarial Notation

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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. For example, in the case of nla,, a is the function symbol when the change is to occur or what it and x, m and n are the parameters. is going to be, a traditional prospective The Halo Notation is very concise and unambiguous and therefore it can be adjusted premium approach is suggested. easily read and quickly understood. A more diffused notation would be somewhat This approach should assume changes time-consuming to read and may not be as quickly understood. Indeed, this is not stated numerically in the policy perhaps the main reason why the Halo Notation has gallantly survived over 130 would not occur. When a change in pre- years. However, the Halo Notation cannot be easily typed with common typing miums or benefits does occur, new ad- devices nor can it be easily incorporated into computer programmes. justed premiums should be calculated In an attempt to remedy the shortcomings of ‘the Halo Notation with respect such that their present value equals the to programmability, a number of actuaries have suggested linearizing the actuarial present value of future benefits less the notation. In fact, since 1968, at least nine papers have been published ,on the subject. current minimum cash value plus any These papers are: new expense allowance resulting from 1. Proposals for an International Actuarial Publication Language and its the change, again assuming no further Representation in Computer Compatible Form by Carl Boehm (Germany), Georg changes beyond the point of recalcula- Reichel (Germany) et al. published in the Transactions of the XVIIZ International tion. This procedure would be used for Congress of Actuaries, Munich 1968. minimum values for most life-cycle and 2. A New Actuarial Notation by the General Functions Sub-Committee of the cost-of-living policies. Institute of Actuaries of Australia and New Zealand, published in October 1971. ‘I’he Committee looked beyond the st.~ccial plans that have been discussed 3. ACT, An Actuarial Programming Language by David R W. Jamieson (Can- and recommended that for unique poli- ada), published in the January 1972 issue of ‘The Actuary. It must be noted that cies not yet developed, a central techni- ACT is not meant to be a publication language but only a programming language. cal entity (such as the NAIC Central 8. Some Proposals for a Revision of the Internationul Actuarial Notation by Office) could be empowered to review P. J. Turvey (Great Britain) published in the Journal of the Znstitute of Actuaries policies to determine if they are actu- Students’ Society March 1972. arially srund and meet certain standards 5. Proposals for an International Actuarial Publication Langwge by Carl Boehm of equity and to approve other technical (Germany), J. Adams (Belgium) et al. published in the Transactions of the XIX aspects. This approach would facilitate International Congress of Actuaries, Oslo 1972. approval of complex policies and would 6. A Contribution to the Discussion on a New International Actuurid Notation promote feasibility of product design by J. Engelfriet (Netherlands) and A.I.M. Kool (Netherlands) published in the while decreasing risk of abuse. October 1973 issue of the BLATTER. This reviewer is somewhat disappoint- 7. An Actuarial Notation Based on Symbolic Logic by G. C. Taylor (Australia) ed that the Committee did not recom- Research Paper No. 50 published by the Macquarie University in April 1974. mend also allowing the use of an assump- 8. Thoughts on the Harmonization of Some Proposals for a New International tion of a percentage increase in the in- Actuarial Nolation by C. Boehm (Germany), J. Engelfriet (Netherlands) et al. pub- dex in the case of cost-of-living increases lished by the authors in 1975. so that minimum values could be deter- mined at issue. The proposed minimums 9. A Revised Actuurid Notation. A suggestion by the Notation Sub-Committee are complex and could be very difficult of the Institute of Actuaries of Australia and New Zealand (Edition 10, October for the consumer to understand. How- 1975). ever, the proposed minimums would The table below shows four of the most commonly used actuarial functions in accommodate a modification of the in- Halo Notation and in linearized notation as suggested in the papers listed above. (Continued OR page 5) (Continued OR page 5) March, I.976 THE ACTUARY Page Five l (ml. Unruh Halo Notation a, AZ ax:4 Ax:;;l (Continued from puge 4) Boehm/Reichel at,.) A fr) a(x;n;m) AE(x;n) dex accumulation method for a cost-of- Australia/New Zealand livine ~ policy where the death benefit (1971) a(,) bfb,n) B(x,n) and cash values escalate with the cost- of-living but premiums remain level. Jamieson ANXNMXNM AXNXN (See Life Insurance Bnsed on the Consul Turvey apnm (x,n,m) an(v) mer Price Index, by Bragg and Stone- Boehm/Adams a(v,k) AE(x,d cipher, TSA XXII, p. 351). Presumably Engelfriet/Kool ‘a- (x,n,k) AE (x,4 the minimum cash value defined by Taylor l A(xhLn) (2) above could not be greater than tbe Sinthesis comparable cash value for a level face amount policy at the same duration, and Boehm/Engelfrite (k)a(x:n) A(v) for the attained death benefit at that Australia/New Zealand a(x, #n, f=m) Ab,#n) duration. It would be preferable and (1975) provide a greater flexibility if this type of policy could be allowed to be approv- l Taylor’s paper does not give sufficient information to complete this notation. ed by the suggested central entity set up In 1972, the President of the International Actuarial Association appointed by the NAIC or state regulators. the Sub-Committee on Notation with the responsibility of gathering opinions on the The Committee is aware of the criti- desirability of developing a new actuarial notation. The two basic questions that cism of the current non-forfeiture law, the Sub-Committee must answer ‘are: that it allows certain products in today’s marketplace which meet the letter but (a) Is it desirable to linearize the International Actuarial Notation, and, if so, perhaps not the spirit of the law and the is there sufficient interest amongst the various national actuarial bodies to Report suggests ways to minimize these replace the Halo Notation with a linearized one? abuses. (b) Whether or not linearization is desirable and/or acceptable, should the The Committee re-examined the ex- scope of the actuarial notation be extended to cover fields such as pensions, pense all,owances in the present law be- l disability, demography, social insurance and non-life insurance? cause these were developed more than It would appear to be most desirable to extend the scope of the actuarial thirty years ago. More modern estimates notation to other fields. The linearization issue, however, seems to be quite con- of excess of first year expenses over re- troversial. There are three distinct points of view: newal expenses would likely decrease as 1. The traditionalists feel that the Halo Notation has served the profession well a percentage of face amount and increase since it first was officially adopted by the Institute of Actuaries over 100 years ago. as a percentage of premium. The Com- Furthermore, the notation is concise, it can be easily read and understood and why mittee concludes that appropriate mod- change it simply to accommodate today’s computers? Indeed, computers of five or ern expense factors would be bracketed ten years from now may be able to make use of peripheral equipment which will by the following for a whole life plan: enable them to read and print the Halo Notation easily. Low: $10 per $1,000 plus 90% of 2. The reformists point out that common printing devices cannot cope with 1958 CSO 3%“/0 net premiums the Halo Notation. This shortcoming increases substantially the cost of printing High: $20 per $1,000 plus 150% of actuarial textbooks, papers, etc.
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