21 August 2014
Due to a low birth rate many countries need immigration to sustain a given population size. The age-distribution of the immigrants has a strong effect on the economy, in particular the social security system. We investigate the optimal immigration age-patterns within certain bounds. The main qualitative result is that under certain conditions the optimal policy is time-invariant.
Mathematically, we deal with an age-structured optimal control problem on the infinite horizon, with non-local integral states. A new type of transversality condition (the idea stems from recent work by S. Aseev and V. Veliov) was used to identify the correct solution of the adjoint system.
This approach is not only feasible for this particular problem but in general for age-structured optimal control system on the infinite horizon.
C. Simon, B. Skritek, V. Veliov (2013): Optimal immigration age-patterns in populations of fixed size. J. Math. Anal. Appl. 405 (2013) 71-89.
B. Skritek, V. Veliov (2014): On the infinite-horizon optimal control of age-structured systems. Submitted. Working paper electronically available at http://orcos.tuwien.ac.at/fileadmin/t/orcos/Research_Reports/2014-03.pdf
Last edited: 21 August 2014
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