NOTES ON OTHER ACTUARIAL JOURNALS

Transcription

1 237 NOTES ON OTHER ACTUARIAL JOURNALS BY H. L. SEAL, B.Sc., PH.D., F.F.A., A.I.A., A.S.A., J. HAMILTON-JONES, M.A., F.I.A., F.S.S., AND C. J. CORNWALL, M.A., F.I.A., F.S.S. BELGIUM Bulletin de l Association des Licenciés en Sciences Actuarielles issus de l Université Libre de Bruxelles, No. 2, 1961 TEGHEM, J. Sur les conditions d applicabilité de la méthode de moindres carrés à l estimation d une relation linéaire, pp MARTIN, L. Étude biométrique de la natalité en Belgique sur la base du recensement de 1947, pp HUYBERECHTS, S. Les principaux critères de décision, pp LAMBERT, H. Quelques aspects du problème de la ruine, pp HIERNAUX, W. La mortalité des assujettis à la Sécurité Sociale Belge. Expérience , pp FRANCE Bulletin Trimestriel de l Institut des Actuaires Français, 72, 1961 URTASUN, J. Contribution à l étude actuarielle des operations financières, pp A fundamental analysis (based on earlier French thought) of the problem of comparing fixed interest securities. The analysis includes securities with future payments tied to a price index. The objections to the usual compound interest technique are that the equation for the rate of interest does not necessarily produce a unique solution in a practical case and that the underlying theory that one could (or even desires to) re-invest income at the original rate is invalid. After arguing the merits of pure simple interest the author introduces a system of weighting interest items to represent the relative attraction of payments in the immediate future and remote payments. He reaches the formal result that the weights produce the same criterion (viz. a weighted yield), as would the assumption that all interest items in the future are reinvested at the mean long-term market rate of interest. Finally, two criteria are put forward which are superior to the weighted yield. The index of comparison which could apply to investments either at simple interest or compound interest is a function of the weighted yield and the mean market rate of interest. The function is constructed so as to eliminate the assumption that receipts in the future earn interest at the initial yield. The coefficient of elasticity shows the relative sensitivity of the yield to changes in the price indexes, system of weights or other underlying functions. Numerical examples are given. BERNARD, A. Rapport sur la Thèse de M. Bonneau, intitulée Etude d'une méthode pour la comparaison des emprunts indexés, pp

2 238 Notes on other Actuarial Journals BONNEAU, P. Étude d une Méthode pour la Comparaison des Emprunts Indexés, pp The issue of index-tied securities in France effectively commenced in 1952, and finished in Nevertheless, the issues are still actively dealt in, and a study of the many types of index used, and their effect on the value of the securities is made in this article. PETIT, J. Indications sur les tables de mortalité servant de bases aux tarifs 1958 des assurances sur la Vie, pp Current mortality tables prescribed by law for French Life companies are the population tables PM 1946/49 in the case of assurances, PF 1946/49 in the case of pure endowments and similar contracts. Both tables were adjusted and graduated, for convenience, by a Makeham formula. Special treatment was necessary for ages less than 21. The article gives full details. LEMONNIER, A. Réserve pour risques courus, généralisation, pp Deals with the calculation of outstanding claims reserves for non-life business in the special class of risk for which settlement may be delayed for a very long period (for 30 years in the example considered). Outlines the possibilities of generalizing the method to other classes of risk. WETZEL, J. M. Bases du calcul des primes de l assurance groupe d indemnités journalières, pp The form of group sickness insurance considered involves single premiums providing benefits for a maximum of one year s sickness including a waiting period. The sickness must commence within the policy year: all sickness within the year is considered as linked-up. Interest is ignored, and the premium calculated by reference to the claim frequency and the expected number of days of incapacity. The latter was calculated by fitting the frequency distribution: GERMANY Blätter der Deutschen Gesellschaft für Versicherungsmathematik, 5, 1961 MÜNZNER, H. Alte und neue Extremalprobleme in der Wirtschaft, pp Discusses, with examples, the optimization problems encountered in operational research. PETRUCCI, G. Der jahrliche Geschäftsbericht eines Lebensversicherungsbetriebes in Italien, pp The first of a series of articles describing the statutory requirements in different countries governing the accounts and valuations of life offices. SCHÖBE, W. Fortschreibung geschlossener Bestände von Versorgungsberechtigten mittels Kommutationszahlen, pp Commutation functions of the general form

3 Notes on other Actuarial Journals 239 can be used to estimate the number of surviving annuitants at a future point of time, starting from a fixed number of active persons subject to retirement at age z or earlier because of ill health. Excluding the wives of active persons, the function leads to similar estimates of the number function of wives and widows and the to estimates of the number of wives with husbands surviving. By subtraction the number of widows can be obtained. The method can be extended to include marriages after retirement. BERGER, G. Zur Bewertung ratierlicher Renten, pp Basic formulae derived from Newton s advancing difference formula are used to test some approximations to the values of immediate and reversionary annuities payable more frequently than once a year. TRÖBLIGER, A. Mathematische Untersuchungen zur Beitragsrückgewähr in der Kraftfahrversicherung, pp Claims data from a motor insurance office are shown to be non-homogeneous after allowing for known objective factors such as type of vehicle and location of registration and the differences are attributed to subjective risks. Reductions in, and supplements to, premiums are therefore based on previous individual experience. The no-claim bonus and additional premiums necessitated thereby are discussed. SCHNELL, P. and STEPHAN, D. Einige ALGOL-Programme PP für Sortierverfahren, MAHN, H. Eine Bemerkung zu einem Existenzsatz für Gleichgewichtspunkte bei n-personenspielen, pp , 1962 O BRIEN, C. M. Die gesetzlichen Bestimmungen über die Rechnungslegung eines Lebensversicherungsunternehmens in Grossbritannien, pp ALTING VON GEUSAU, JHR. G. M. M. Rechnungslegungsvorschriften für Lebensversicherungsunternehmen in den Niederlanden, pp This and O Brien s paper above are two further contributions to the series of international comparisons of the statutory requirements for the valuation and accounts of life offices. RUFENER, E. Restgliedabschätzungen für Lidstonesche Approximationen, pp Expressions are derived for evaluating the error involved in replacing REICHEL, G. Bemerkungen über Altersunterschiede von Ehepaaren, pp Develops a method for estimating the average age-difference in all marriages from data for those terminated by the death of one of the partners.

4 240 Notes on other Actuarial Journals KUPPER, J. Wahrscheinlichkeitstheoretische Modelle in der Schadenversicherung. Teil I: Die Schadenzahl, pp The first part of a systematic study of different models in non-life insurance, dealing with the distribution of the number of claims. SCANDINAVIA Skandinavisk Aktuarietidskrift, 43, 1960 HANSEN, C. Über einige Sätze und Formeln der Mathematik der Lebensversicherung auf ein Leben, pp A series of general theorems about assurances with variable premium and sum assured. BOYD, A. V. Gurland s inequality for the gamma function, pp A mathematical (i.e. non-statistical) proof. PHILIPSON, C. The theory of confluent hypergeometric functions and its application to compound Poisson processes, pp Advocates the use of hypergeometric functions in the theoretical analysis, the reduction of observations, and the testing of hypotheses connected with compound Poisson processes. BORCH, K. The safety loading of reinsurance premiums, pp If two insurance companies are negotiating to conclude a reciprocal reinsurance treaty the author has shown that there may exist a unique treaty optimal to both (see vol. 43, pp ). The arguments are here extended to any number of companies. AJNE, B. On the estimation of the time mean-value of a stationary process, pp A finite linear combination of equidistant observed values is chosen to minimize asymptotically the mean square error. SPAIN Anales del Instituto de Actuarios Españoles, Segunda Epoca, 1, 1961 This new series of the Anales commences with a number containing, inter alia: (1) Extracts from Statutes regarding the education, professional organization and technical responsibilities of Spanish actuaries. (2) The Rules of the Institute of Spanish Actuaries. (3) Code of Professional Conduct. (4) Governing body list of members. (5) List of members of the Institute. SWITZERLAND Mitteilungen der Vereinigung schweizerischer Versicherungsmathematiker, 61, 1961 AMMETER, H. Risikotheoretische Grundlagen der Erfahrungstarifierung, pp Examines a method of experience rating for group assurances involving a premium refund is the net premium, S the amount of claims and and β are chosen so that the expected value of

5 Notes on other Actuarial Journals 241 G is equal to the security loading in the premium both when the expected number of claims is correctly assessed and under certain alternative hypotheses. MEIER, H.-P. Bearbeitung des Witwenrentenfaktors der Grundlagen für Gruppenversicherungen mit elektronischen Rechenmaschinen, pp BAUMGARTNER, U. Abschätzung von Reserven mit spieltheoretischen Methoden, pp The method of Benjamin and Bennett (J.I.A. 84, 1) for the determination by linear programming of limits to the valuation reserve is extended to cover policies with different maturity ages as well as different terms. The optimal choice of a mean value within the given limits is discussed in terms of the theory of games. CAPT, E. Un aspect du problème du risque, pp A discussion, with examples, of the circumstances in which claims are not mutually independent. SCHÖBE, W. Zum Lucasschen Ehepaarproblem, pp YNTEMA, L. Äquivalenzrechnung, pp A generalized treatment of questions involving compound interest or life contingencies is proposed, proceeding analytically from the principle of the equivalence of payments and receipts at different points in time. The two subjects would thus be developed uniformly, with a suitably chosen notation and terminology in common. SUMITSUJI, O. Some Elementary Researches in the Mathematics of Life Insurance (III), pp ASTIN The A.S.T.I.N. Bulletin, 2, 1962 (Publication of the Astin Section of the Permanent Committee for International Actuarial Congresses) This issue deals with two of the subjects discussed at the second international colloquium of ASTIN arranged by the Swedish Actuarial Society at Rättvik, in June Subject one: Distribution of the amount of one claim. BANASINSKI, A. and WANATOWSKI, A. Remarks on statistical distribution of intensity of chance damages, pp Statistics are presented on the extent of damage of rural buildings damaged by fire and compulsorily insured. The data are Polish. BENCKERT, L.-G. The lognormal mode for the distribution of one claim, pp BENKTANDER, G. Notes sur la distribution conditionée du montant d'un sinistre par rapport à l hypothèse qu il y a eu un sinistre dans l assurance automobile, pp Compare the paper by the author and C. O. Segerdahl in the proceedings of the Sixteenth International Congress of Actuaries. CANNELLA, S. Variation de la prime d assurance de l assistance pharmaceutique en fonction de la participation de l assuré au coût de l assistance, pp

6 242 Notes on other Actuarial Journals COPPINI, M. A. A propos de la distribution des cas de maladie entre les assurés et par rapport à la durée, pp Analysis of Italian experience in the field of Social Insurance. LATSCHA, R. Distribution accidents, pp du coût d un sinistre dans l assurance sociale contre les Subject three: Problems in motor insurance. BANASINSKI, A. Optimum structure of trends of activities to prevent chance damages, pp DELAPORTE, P. Sur l efficacité des critères de tarification accidents d automobiles, pp de l assurance contre les LANTELI, G. Novelties in Swedish Automobile Insurance Rating, pp The most important feature of the new schedule is the subdivision with regard to annual mileage. PESONEN, E. A numerical method of finding a suitable bonus scale, pp THÉPAUT, A. Quelques reflexions sur la réforme du tarif français d assurance automobile, pp CANNET, A. Assurance automobile statistique et tarifs pp MASTERSON, N. E. Problems in motor insurance claim reserves, pp PENTIKÄINEN, T. Reserves of motor-vehicle insurance in Finland, pp PENTIKÄINEN, T. Reinsurance of third party motor insurance and motor insurance in Finland, pp