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Eine Bemerkung zur Beitragszahlung versus Kalkulation in der Krankenversicherung.
Abstracts and Reviews
First a general risk theoretical methodology is developed to determine fluctuation loadings dependent on the size of the collective, for homogeneous collectives as well as for heterogeneous ones. A pragmatic method is derived for the latter case, too. Then the methods are carried over to the case of sickness insurance paying attention to the condition that the solution has to be within the existing structure of calculation. The paper is closed with an empirical (Author) study. Keywords:
Fluctuation
Loading,
053052 (M30, BlO) Dread-Disease-Deckungen. Leistungsangebot in der Rechnungsgrundlagen Liirper J., Liittgen
Sickness Insurance.
Ein
erweitertes
Lebensversicherung
-
fdr Deutschland. D., Trunk S., Kbln, Bliitter
Technical
053053 (M30, MlO) An application of exponential premium
models
in
rating.
Renshaw Bulletin
A.E.,
The City University,
London,
Astin
23, nr. I, 1993, pp. 145-147.
A practical method of allowing compound Poisson modelling discussed. Keywords:
Premium
Rating,
Distributions, Generalized Variance Function.
for covariates in distributions is (Author)
Compound
Linear
Models,
Annual Premium,
EXPERIENCE
THEORY,
Bases, Premium.
dispersion
Keywords:
M3Z:
So-called Dread Disease covers represent an extension to traditional Life Assurance benefits. Payment of the sum assured results not only in case of death but also in case certain serious diseases occur. This paper first describes an actuarial model for the pricing of this type of cover. Then the authors demonstrate which statistical date is required in order to obtain technical basis, and how specific technical bases for the German market can be derived from available German statistics and transfer of international (Authors) experience. Dread Disease,
In Germany, the premium in Private Health Insurance is usually calculated as an annual premium, payable in advance at the beginning of the insurance year. In accordance to the exemplary insurance conditions edited by the German association of Private Health Insurances, annual premiums are also payable by installments that are considered to be delayed until the following date of payment. Monthly premiums are computed by simply division of annual premiums; usually no additional premiums are required for payment by installments. Consequently, there is a loss, and in this paper the expected loss is partitioned in relation to its causes. Furthermore the authors show its influence on the annual accounting. (Authors) Private Health Insurance.
der
Deutsche Gesellschaft fiir Versicherungsmathematik, Band Xu, Heji 2, oktober 1991, pp. 169-182.
Keywords:
157
Poisson Power
053054 (M30, B21) Eine Bemerkung zur Beitragszahlung versus Kalkulation in der Krankenversicherung. Brand N., Jungwirth H., Miinchen, Bliitter der Deutsche Gesellschaft fiir Versicherungsmathematik, Band Xx, Heft 2, april 1992, pp. 3 73-3 76.
RATING,
BONUS-MALUS
053055 (M31) Lineare Filtration
CREDIBILITY
SYSTEMS
und Kredibilitltstheorie
(Linear
filtration and credibility theory). Hiss K., University of Basel, Bulletin of the Swiss Association of Actuaries,
Vol. 91. I, 1991, pp. 8.5-103.
The paper is divided into two parts. First a class of stochastic processes is presented which is considered in more detail later. It is shown that the estimation of random variables in the Hilbert space L,(R,gP) can be looked upon as a projection onto a suitable subspace. There follows a short presentation of the linear filtration theory and its main result, the theorem of Kalman. In the second part the results from filtration theory are applied to obtain credibility estimators in actuarial models. Following the presentation of a general credibility model, the classical models of Biihlmann (1967) andBtihlmann/Straub( 1970), the linearregression model of Hachemeister (1975) and a special case of the exponential regression model of de Vylder (1986) are carried over to the continuous case, and the credibility estimator 2 is calculated by means of the Kalman filter method. In all four models a result of the form J=(lK)p+KY is obtained with the a priori mean p, a weighted average Y of the observations and a factor K of norm between 0 and 1. The results determined in the continuous case by means of the Kalman filter correspond exactly to those obtained by the discrete approach. Finally, two new credibility models are presented. (A. Gisler) Keywords:
Kalman Filter, Linear Filtration,
Credibility.
First a general risk theoretical methodology is developed to determine fluctuation loadings dependent on the size of the collective, for homogeneous collectives as well as for heterogeneous ones. A pragmatic method is derived for the latter case, too. Then the methods are carried over to the case of sickness insurance paying attention to the condition that the solution has to be within the existing structure of calculation. The paper is closed with an empirical (Author) study. Keywords:
Fluctuation
Loading,
053052 (M30, BlO) Dread-Disease-Deckungen. Leistungsangebot in der Rechnungsgrundlagen Liirper J., Liittgen
Sickness Insurance.
Ein
erweitertes
Lebensversicherung
-
fdr Deutschland. D., Trunk S., Kbln, Bliitter
Technical
053053 (M30, MlO) An application of exponential premium
models
in
rating.
Renshaw Bulletin
A.E.,
The City University,
London,
Astin
23, nr. I, 1993, pp. 145-147.
A practical method of allowing compound Poisson modelling discussed. Keywords:
Premium
Rating,
Distributions, Generalized Variance Function.
for covariates in distributions is (Author)
Compound
Linear
Models,
Annual Premium,
EXPERIENCE
THEORY,
Bases, Premium.
dispersion
Keywords:
M3Z:
So-called Dread Disease covers represent an extension to traditional Life Assurance benefits. Payment of the sum assured results not only in case of death but also in case certain serious diseases occur. This paper first describes an actuarial model for the pricing of this type of cover. Then the authors demonstrate which statistical date is required in order to obtain technical basis, and how specific technical bases for the German market can be derived from available German statistics and transfer of international (Authors) experience. Dread Disease,
In Germany, the premium in Private Health Insurance is usually calculated as an annual premium, payable in advance at the beginning of the insurance year. In accordance to the exemplary insurance conditions edited by the German association of Private Health Insurances, annual premiums are also payable by installments that are considered to be delayed until the following date of payment. Monthly premiums are computed by simply division of annual premiums; usually no additional premiums are required for payment by installments. Consequently, there is a loss, and in this paper the expected loss is partitioned in relation to its causes. Furthermore the authors show its influence on the annual accounting. (Authors) Private Health Insurance.
der
Deutsche Gesellschaft fiir Versicherungsmathematik, Band Xu, Heji 2, oktober 1991, pp. 169-182.
Keywords:
157
Poisson Power
053054 (M30, B21) Eine Bemerkung zur Beitragszahlung versus Kalkulation in der Krankenversicherung. Brand N., Jungwirth H., Miinchen, Bliitter der Deutsche Gesellschaft fiir Versicherungsmathematik, Band Xx, Heft 2, april 1992, pp. 3 73-3 76.
RATING,
BONUS-MALUS
053055 (M31) Lineare Filtration
CREDIBILITY
SYSTEMS
und Kredibilitltstheorie
(Linear
filtration and credibility theory). Hiss K., University of Basel, Bulletin of the Swiss Association of Actuaries,
Vol. 91. I, 1991, pp. 8.5-103.
The paper is divided into two parts. First a class of stochastic processes is presented which is considered in more detail later. It is shown that the estimation of random variables in the Hilbert space L,(R,gP) can be looked upon as a projection onto a suitable subspace. There follows a short presentation of the linear filtration theory and its main result, the theorem of Kalman. In the second part the results from filtration theory are applied to obtain credibility estimators in actuarial models. Following the presentation of a general credibility model, the classical models of Biihlmann (1967) andBtihlmann/Straub( 1970), the linearregression model of Hachemeister (1975) and a special case of the exponential regression model of de Vylder (1986) are carried over to the continuous case, and the credibility estimator 2 is calculated by means of the Kalman filter method. In all four models a result of the form J=(lK)p+KY is obtained with the a priori mean p, a weighted average Y of the observations and a factor K of norm between 0 and 1. The results determined in the continuous case by means of the Kalman filter correspond exactly to those obtained by the discrete approach. Finally, two new credibility models are presented. (A. Gisler) Keywords:
Kalman Filter, Linear Filtration,
Credibility.