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Ein Ergodensatz der Personenversicherungs-mathematik und seine Anwendung in der betrieblichen Altersversorgung.
152
Abstracts and Reviews
retirement and widow’s annuity. 5. Summarizing explanations including a final example. A major point in the discussion is that the author makes use of a stochastic approach and simulations. (W.R. Heilmann) Keywords: Pension Reserves, Principle of Caution, Expectancies. 053031 (M12, B13) ober die Variation von Steuerungsgrofien in Rentenversicherungssystemen (On the variation of control parameters in pension systems). Jensen G., Munchen, Blatter der Deutsche Gesellschaft fur Versicherungsmathematik, Band Xu, Heft 4, oktober 1992, pp. 405423. In pension systems with full or partial funding, in contrast to the pay-as-you-go method, it is possible to create a potential for the increase of benefits by a decrease of the reserve, leaving the contributions unchanged. Assessment systems like the French “repartition par points de retraite” are especially suited for these measures. Two procedures are compared. The first results in making it more expensive to acquire additional points, thereby in the assessment process increasing the value of points acquired in the past, too. The second is to lower the valuation of the future liabilities, which is most simply achieved by using a higher rate of interest in the calculation of present values; this sets assets free which may be used to cover increases of benefits. The method of investigation is direct calculation, based on the evolution equation of the dynamical system, and is independent of special assumptions like exponential behavior. To make the rather involved calculations more transparent, the calculus of Stieltjes-Scharf integrals is used. The variations of the parameters are given in the form sh, the consequences are studied in linear approximation, i.e. using a development eH+O(?). It turns out that the consequences of both methods are comparable in principle, though the first method yields a stronger increase in benefits in relation to the consumption of assets. The reason is that the burdens are distributed more uniformly and fairly among the future generations. Moreover, the first method seems to enable a better controlling of the process of asset (Author) reduction. Keywords: Reserve, Future Liabilities. 053032 (M12, B13) Ein Ergodensatz
der
Personenversicherungs-
mathematik und seine Anwendung in der betrieblichen Altersversorgung. Neuburger E., von Chossy R., Mtinchen, Blatter der Deutsche Gesellschaft fir Versicherungsmathematik, Band Xu, Heft 2, oktober 1991, pp. 227-239. It is shown that the sum of the premiums (calculated with interest zero) of the beneficiaries of a benefit plan equals the sum of the benefits (trend-removed) “in the long run”, i.e. in steady state (permanent payments). The permanent payments are suited as a measure of the volume of the obligations (“Dotierungsrahmen”) of a benefit plan; by means of the proved theorem it can be calculated in an easy manner. (Authors) Keywords: Benefit plan. 053033 (M12, B21) The impact of AIDS on disability insurance. Holzwarth A., Weyer J., Koln, Blatter der Deutsche Gesellschaft fur Versicherungsmathematik, Band Xu, Heft I, april 1991, pp. l-30. In spite of many appeasing statements, the registered AIDS cases keep rapidly growing. At the end of the year 1990 there where about 5.600 reported cases of full-blown AIDS in the Federal Republic of Germany and 160.000 registered cases in the USA, not considering the high rate of underreporting. This development will necessarily cause a dynamically increasing risk for life and disability insurance. Any bases of calculations have to take into account the additional disability caused by AIDS. In the present article the authors estimate the additional risk of AIDS by means of some mathematical models and computer simulation. The corresponding actuarial adjustment is founded on the new bases of calculation. In the framework of these new bases the probability of death (for disables) depends on two time parameters: age and duration (anciennity) of disability of the sample person: As the risk of AIDS is dynamically increasing, the mortality of disables adjusted to AIDS is also varying according to the respective calendar year. Their analysis shows that disability insurance of females will definitely develop more favorably than the corresponding insurance of males. The following point is an essential result of the present article: In particular, short term contracts in disability insurance of men will require a seriously increased premium in order to guarantee the benefit payment. This shift concerning short term contracts is due to the fact that in case of disability caused by AIDS the insured duration of benefit payment (Authors) will be widely exhausted.
Abstracts and Reviews
retirement and widow’s annuity. 5. Summarizing explanations including a final example. A major point in the discussion is that the author makes use of a stochastic approach and simulations. (W.R. Heilmann) Keywords: Pension Reserves, Principle of Caution, Expectancies. 053031 (M12, B13) ober die Variation von Steuerungsgrofien in Rentenversicherungssystemen (On the variation of control parameters in pension systems). Jensen G., Munchen, Blatter der Deutsche Gesellschaft fur Versicherungsmathematik, Band Xu, Heft 4, oktober 1992, pp. 405423. In pension systems with full or partial funding, in contrast to the pay-as-you-go method, it is possible to create a potential for the increase of benefits by a decrease of the reserve, leaving the contributions unchanged. Assessment systems like the French “repartition par points de retraite” are especially suited for these measures. Two procedures are compared. The first results in making it more expensive to acquire additional points, thereby in the assessment process increasing the value of points acquired in the past, too. The second is to lower the valuation of the future liabilities, which is most simply achieved by using a higher rate of interest in the calculation of present values; this sets assets free which may be used to cover increases of benefits. The method of investigation is direct calculation, based on the evolution equation of the dynamical system, and is independent of special assumptions like exponential behavior. To make the rather involved calculations more transparent, the calculus of Stieltjes-Scharf integrals is used. The variations of the parameters are given in the form sh, the consequences are studied in linear approximation, i.e. using a development eH+O(?). It turns out that the consequences of both methods are comparable in principle, though the first method yields a stronger increase in benefits in relation to the consumption of assets. The reason is that the burdens are distributed more uniformly and fairly among the future generations. Moreover, the first method seems to enable a better controlling of the process of asset (Author) reduction. Keywords: Reserve, Future Liabilities. 053032 (M12, B13) Ein Ergodensatz
der
Personenversicherungs-
mathematik und seine Anwendung in der betrieblichen Altersversorgung. Neuburger E., von Chossy R., Mtinchen, Blatter der Deutsche Gesellschaft fir Versicherungsmathematik, Band Xu, Heft 2, oktober 1991, pp. 227-239. It is shown that the sum of the premiums (calculated with interest zero) of the beneficiaries of a benefit plan equals the sum of the benefits (trend-removed) “in the long run”, i.e. in steady state (permanent payments). The permanent payments are suited as a measure of the volume of the obligations (“Dotierungsrahmen”) of a benefit plan; by means of the proved theorem it can be calculated in an easy manner. (Authors) Keywords: Benefit plan. 053033 (M12, B21) The impact of AIDS on disability insurance. Holzwarth A., Weyer J., Koln, Blatter der Deutsche Gesellschaft fur Versicherungsmathematik, Band Xu, Heft I, april 1991, pp. l-30. In spite of many appeasing statements, the registered AIDS cases keep rapidly growing. At the end of the year 1990 there where about 5.600 reported cases of full-blown AIDS in the Federal Republic of Germany and 160.000 registered cases in the USA, not considering the high rate of underreporting. This development will necessarily cause a dynamically increasing risk for life and disability insurance. Any bases of calculations have to take into account the additional disability caused by AIDS. In the present article the authors estimate the additional risk of AIDS by means of some mathematical models and computer simulation. The corresponding actuarial adjustment is founded on the new bases of calculation. In the framework of these new bases the probability of death (for disables) depends on two time parameters: age and duration (anciennity) of disability of the sample person: As the risk of AIDS is dynamically increasing, the mortality of disables adjusted to AIDS is also varying according to the respective calendar year. Their analysis shows that disability insurance of females will definitely develop more favorably than the corresponding insurance of males. The following point is an essential result of the present article: In particular, short term contracts in disability insurance of men will require a seriously increased premium in order to guarantee the benefit payment. This shift concerning short term contracts is due to the fact that in case of disability caused by AIDS the insured duration of benefit payment (Authors) will be widely exhausted.