Pricing with respect to the number of policies in force in health insurance
Abstract
The number of policies in force of a certain health insurance tariff is of crucial importance for accurate pricing of this tariff. The smaller the number of policyholders is the bigger the variance of the average claims per head gets.
We present a method to compute a “minimal number” of policies in force. This method uses the empirical mean and the empirical variance of the distribution of claims of a given tariff. By construction of this method the random fluctuation of the average claims per head is reduced to a predefined and acceptable level if the number of policies in force of a tariff is bigger than this “minimal number” (with a given level of uncertainty).
In case the number of policies in force of a certain tariff falls bellows the aforementioned minimal number, the statistical basis for the pricing of this tariff has to be enlarged, for example by using external data. This paper presents an alternative approach to this problem by creating the concept of “collectives of tariffs”. By this we mean a number of tariffs with similar coverage. After an appropriate scaling with respect to the differences in the coverages the tariffs together form a virtual tariff that can be used for pricing of all tariffs in the collective.
The German Association of Actuaries (Deutsche Aktuarvereinigung or DAV) is the professional body representing actuaries and Appointed Actuaries in Germany. It creates the underlying conditions enabling its members to practice their profession properly and in a technically sound manner as well as engaging in constant dialogue with all relevant national and international institutions.
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