The author determines the decrement tables leading, for endowment assurances, to the hyperbolic reserve function ofJecklin’s reserve model. He shows in particular that, for a given maturity age (s), a necessary and sufficient condition for the reserve to follow a rectangular hyperbola with asymptotes parallel to the co-ordinate axes is given by the following mortality laws a $$\begin{gathered} x) = D_x = v^x l(x) = e^{ - \delta x} l(x): \hfill \bar f(x) = k\left( {l - \frac{x}{c}} \right)\left( {l - \frac{x}{s}} \right)^{\lambda (c - s) - 1} e^{ - \lambda x} \hfill \end{gathered} $$ and b $$f(x) = K(c - x)\frac{{\Gamma (s - x)}}{{\Gamma (\sigma - x)}}(1 - \lambda )^x ,$$ according to whether the reserve is defined in (a) a continuous or (b) a discontinuous way. If the above rectangular hyperbola is replaced by a non-rectangular hyperbola with one asymptote parallel to the ordinate then the functions (a) and (b) are replaced by a $$f^ * (x) = k\left( {l - \frac{x}{c}} \right)\left( {l - \frac{x}{s}} \right)^{\lambda A - 1} \left( {l - \frac{x}{{s + a}}} \right)^{\lambda B - 1} $$ and b $$\begin{gathered} f^ * (x) = K(c - x)\frac{{\Gamma (s - x \Gamma (s + a - x)}}{{\Gamma (s - \alpha + 1 - x) \cdot \Gamma (s - \beta + l - x)}} \hfill = K(c - x)(s - 1 - x)^{(\lambda A - 1)} (s + a - 1 - x)^{(\lambda B - 1)} \hfill \end{gathered} $$ These functions include de Moivre’s law as a special case, leading to a hyperbolic reserve curve for every maturity age. The reserves defined by these functions also include the special cases of rectangular hyperbolic and linear reserves.