Genäherte Bestimmung der mittleren Lebensdauer erhöhter Risiken

Whereas there are many known procedures for the approximate derivation of the premiums and even of the reserves for substandard lives from the values these functions assume for standard risks, no such approximation exists for the complete expectation of life. The author derives a formula which, for the case of multiplicative extra mortality, allows this measure to be computed easily and with an excellent degree of approximation for any substandard life from the corresponding figure for standard lives without reference to the basic computation columns. The formula is obtained by using hyperbolic interpolation and the fact that the series of fractions of the ex columns for standard and enhanced mortality, respectively, can be represented quite accurately by an arithmetical series of second order.