21 August 2014

Lecture on Optimal Control of Size-Structured Populations

Bernhard Skritek gave a talk on "Optimal Control of Age-structured Systems on the Infinite-horizon: Optimal Immigration Age-patterns in a Population of Fixed Size" on 20 August.

Talk abstract:

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

Bernhard Skritek received a Masters Degree vom Vienna University of Technology in Technical Mathematics in 2011. In the same year, he started his PhD thesis at Vienna UT under supervision of Vladimir Veliov, in which he investigates heterogeneous optimal control problems, with a strong focus on transversality conditions for problems on the infinite horizon, as well as Hamiltonian formulations. He recently finished a Bachelor at Vienna University of Economics and Business. Since July he is researcher at the IIASA in a joint project of the ASA and the POP program, which focuses on the effects of a populations heterogeneity on educational decisions and thus on economic growth.

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Last edited: 21 August 2014

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