Modifizierung des kalkulationsverfahrens in der deutschen privaten krankenversicherung (PKV) zur beitragsentlastung älterer versicherter.

Abstracts and Reviews

Bayesian graduation models that substantially ease the prior elicitation burden; it also describes a Monte Carlo integration approach that greatly reduces the computational load. The method is presented in generality and subsequently illustrated with two examples, one from the realm of health insurance and the other from the more traditional graduation context of mortality table construction. It is hoped that the method will stimulate greater use of the Bayesian paradigm (Author) within the actuarial community. Keywords:

Graduation,

Bayesian

Approach,

Monte

Carlo Integration.

PREMIUM, PREMIUM PRINCIPLE, ORDERING OF RISKS

M30:

061018 (M30, B20) Moditizierung des Kalkulationsverfahrens in der deutschen privaten Krankenversicherung(PKV) zur Beitragsentlastung tilterer Versicherter. Jansen B., Kempf P.-D., Deutschland, Transactions of International

Congress

of Actuaries,

Montreal,

Vol. 4,

1992, pp. 117-129.

In Germany private health insurance has been written on a level premium basis with the right to adjust premiums to reflect increasing medical costs. In the recent history the escalating medical costs have necessitated significant permanent premium adjustments. Based on the peculiarity of the system the percentage increases in premiums or contributions has exceeded the increases in the medical costs. This, in particular, has affected the elderly adversely. The companies have tried to limit the increases by voluntary means. This paper discusses two modifications to the premium calculation which formalizes the means the company used to limit premium increases for the elderly. 1. Until now administrative expenses have been charged totally on a percentage of premium basis. This paper suggests that they should be charged on a per policy basis. This causes a significant reduction in premiums for the elderly when health costs are very high. 2. Excess interest earnings on the reserves are accumulated and released at five year intervals commencing at age 65. This release modifies the claims costs significantly and mitigates otherwise required premium contributions for the elderly. (Authors) Keywords: Premium.

Health

Insurance,

Medical

Costs,

Level

69

061019 (M30, M40, B50) Risikotheoretische Analyse des Versicherungsgeschiifts auf der Grundlage eines Stochastischen Gesamtmodells. Zimmermann J., Albrecht P., Deutschland, Transactions Montreal,

of International

Congress

of Actuaries,

Vol. 3, 1992, pp. 27-41.

The present paper develops a model for the (oneperiod) result of a property-liability insurance company, including the components premium income, claim costs, operating expenses, and investment income. Accumulated claims and investment returns are considered as stochastic quantities. Possible correlations between the stochastic components, as well as the connection between investment capital generated by an insurance branch with its reserves cause dependencies between the company earnings, which are not reflected adequately by the usual partial models. The model constructed is evaluated on the basis of an economicalstabilitycriterion constrainingtheprobability that the one-period loss completely consumes the security capital of the company. This evaluation is applied to derive results for three problems: premium calculation, solvency, and capacity. In addition, the problem of an optimal mix of insurance lines and investment assets based on portfolio theoretic considerations as well as the problem of maximizing the company’s profit under risk, given the demand function for insurance protection, are considered. (Authors) Keywords: One-Period-Model, Premium, Solvency. 061020 (M30, B90) Sicherheitszuschliigefur Schadenexzedentenvertrlge. Ergiinzende Ergebnisse. Kremer E., Deutschland, Transactions of International Congress of Actuaries,

Montreal,

Vol. 3, 1992, pp. I79-

186.

The problem of calculating a security loading is reconsidered for the case of an excess-of-loss treaty. Already well-known results are extended and completed. A general formula for the security loading is given for the assumption of Poisson-distributed claims number and generalized Pareto-distributed claims sizes. Furthermore a handy bound is derived for the security loading, being valid for arbitrary claims number and claims size distribution. Finally a formula and a bound are given for the security loading, when taking another model for the claims (Author) process. Keywords:

Loading

Factor, Excess-of-Loss,

Bound.