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Abstract
The author determines the decrement tables corresponding to a given curve of the mathematical reserve for endowment assurances with a given maturity age and thus gives a solution of the inversion problem of reserve theory. The paper starts from a criterion in the form of a differential relation which functions of the three variables t (expired duration), x (age at entry), and n (insurance term) must satisfy in order to represent the mathematical reserve defined in a continuous way. The mortality laws corresponding to linear, hyperbolic, exponential and parabolic reserve curves are determined. In this connection, special investigations are made with respect to Jecklin’s model of hyperbolic reserves (F-method).
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