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Alfred Manes (in Encyclopedia of the Social Sciences, Vol. Assurance defines 8, in 1935, page 95) as a removal of the risk of singles by contributions of many (“The essence of insurance lies in the elimination of the uncertain risk of loss for the individual through the combination of a large number similarily exposed individuals who each contribute to a common fund of premiums sufficient to make good the loss caused any one individual.”). Karl Hax defines assurance as the „level-according cover of an uncertain in detail, on the whole, however, of estimateable monetary expansion on the basis of an intereconomic risk balance“. Insurance concept to Farny: Assurance is the cover, an in detail uncertain, monetary expansion estimateable all together, on the basis of a risk balance in the group and in the time. A legal definition does not exist.

The mechanism of the common Tragung of risks forms the basis of the assurance in a group (pool, portfolio). The advantage of this common Tragung is based on mathematically by the law of the big figures of described legitimacy after which with rising number of events of the same kind the actual exit adapts itself to the expected exit (to the middle value of all possible exits); the dispersion (variability) of the exits around the middle value decreases by rising group size constitutionally, mathematically described by the central limit value sentence. Therefore, the risk of the variation of the exit decreases the more, the greater the group is. This risk-diminishing effect of a common Tragung of risks in a group is called risk balance in the group. In the result thereby becomes the risk of the failure of the risk balance, so that the group does not have enough money to pay all damages, by rising group size smaller and smaller. A big group needs, in the end, proportionally less capital than precaution for such a failure, as a small group or even an individual for his own risk. However, lower capital means above all lower financing expenses and with it the risk balance causes in the group that risks can be secured for all partners more favourably than this would be individually possible.