Description and control of a continuous-time population process

This paper proposes a model or population characterized by a birth process generating individuals and a core process describing the dynamics of each individual in the population. When the core process is a finite-state continuous-time semi-Markov process, one obtains a complete description of the census process, which gives at any time the number of individuals in each state. The problem of optimally controlling the population process through its birth process is then formulated as a problem of optimal control of a jump process in the continuous-time setting. Two examples show how to use the dynamic programming equations obtained in this paper.