A comprehensive study of the linkages between demographic and
economic variables should not only account for vintage specificity
but also incorporate the relevant economic and demographic
decisions in a complete optimal control set-up. A methodological
set-up allowing to reach these objectives is described. In this
framework, time is continuous but agents take discrete timing
decisions. The mixture of continuous and discrete time yields
differential-difference equations (DDEs). It is clearly shown that
the approach allows for a relatively complete and rigorous
analytical exploration in some special cases (mainly linear or
quasi linear models), and for an easy computational appraisal in
the general case.