Welfare analysis of HIV/AIDS: Formulating and computing a continuous time overlapping generations policy model - Jamsheed Shorish (Institute for Advanced Studies (IHS), 2007)
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.
Keywords: C61; C63; D61; 330; optimal control; continuous time overlapping generations; Hamilton-Jacobi-Bellman PDE; finite difference approximation; HIV/AIDS; demographic modeling; Bevölkerungsentwicklung; AIDS; Bevölkerungspolitik; Overlapping Generations; Theorie