On a Functional Equation in Actuarial Mathematics

In 1839, De Morgan gave a mathematical justification of Gompertz’s law of mortality through a composite functional equation, fŽx y. fŽx z. fŽx hŽy, z... A slightly more general version of this equation was studied in 1905 by M. Chini. Both solved their equations in the class of differentiable functions on the real line. Here we solve the equation fŽx. fŽx y. cfŽx gŽy.., which is a generalization of Chini’s equation, on intervals in the class of locally bounded functions and in the class of continuous functions