Welfare analysis of HIV/AIDS : formulating and computing a continuous time overlapping generations policy model

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