Reihe Ökonomie / Economics Series, Institut für Höhere Studien (IHS) 211
We introduce a continuous time overlapping generations demographic model, in which a social planner seeks to generate an optimal policy for influencing the demographic change of the underlying population in a neoclassical growth model. The model has the notable feature that the underlying state space is a continuum, leading to a Hamilton-Jacobi-Bellman PDE system which is defined over a Hilbert space generated by the ages of the population cohorts. In this technical report the dynamic programming problem is presented and the numerical approximation using a finite difference approximation is derived. This analysis is part of a larger research program on welfare analysis and policy development for the HIV/AIDS global pandemic.
optimal control continuous time overlapping generations Hamilton-Jacobi-Bellman PDE finite difference approximation HIV/AIDS demographic modeling