Endogenous Heterogeneity and Periodicity in Dynamic Optimization Problems

01.07.2010 - 31.10.2013
Forschungsförderungsprojekt
Heterogeneity can play a substantial role in the evolution of populations, economic systems, epidemic diseases, physical systems, etc. While this has been well recognized in population or physical contexts, the investigation of the role of heterogeneity in economics is a modern, quickly developing area. Dynamic optimization problems for heterogeneous systems first appeared in the population dynamics literature in the eighties. The development of the respective mathematical theory in the last decade created a new powerful research instrument applicable also in economics, management and social sciences. In this proposal heterogeneous control systems are described mathematically by first order distributed controlled differential equations with non-local dynamics and endogenous side-conditions. The theoretical investigations within the present project are motivated by several problems in economics and management that cannot be addressed by applying the existing theory. One of these problems is to characterize the optimal trade-off between investments in capital accumulation versus technological growth. Here the heterogeneity arises due to the simultaneous availability of a variety of technologies and a variety of consumption goods. Both varieties depend dynamically on the investments in research and development (R&D). The main challenge here is to analyze the determinants of technological change, in particular, the role of the demographic factors for the technological advancement. This problem requires developing the theory of optimal control for heterogeneous systems for which the range of heterogeneity depends dynamically on the control policy. This comprises the first main theoretical goal of the project, which includes optimality conditions, numerical methods, and computational tools, in particular for infinite horizon problems. The project includes a second application of the theory and software developed within this goal, which is the investigation of the fundamental question in the context of climate change and global warming: Can the socially optimal abatement policy for greenhouse gases be "implemented" without any direct emission restrictions, controlling only the composition of the investments in R&D? The heterogeneity arises from the coexistence of technologies with different productivities and emission rates, hence the range of heterogeneity depends on the investment policy. A second theoretical goal of the project is to develop mathematical (analytical and numerical) instruments for the investigation of optimal cyclic heterogeneous processes. One very important motivation for this study is industrial fishing in the oceans. It has been observed that the selective industrial fishing leads to fast detrimental evolutionary changes. A model that is able to capture simultaneously the selectivity of fishing (with respect to size) and the evolutionary changes needs at least two parameters of heterogeneity: size and genetic parameters. There is a certain practical and mathematical evidence that the optimal fishing policy in the corresponding heterogeneous optimal control model is cyclic, and the planned theoretical results should allow to obtain conditions for cyclicity and efficient computation of the optimal solution. Several other fields of application of the results from the two theoretical goals are: multistage dynamic optimization problems involving random events, optimization of advection-reaction processes, health economics, economic geography, etc.

Personen

Projektleiter_in

Projektmitarbeiter_innen

Institut

Grant funds

  • FWF - Österr. Wissenschaftsfonds (National) Austrian Science Fund (FWF)

Forschungsschwerpunkte

  • Mathematical Methods in Economics: 35%
  • Efficient Utilisation of Material Resources: 5%
  • Mathematical and Algorithmic Foundations: 60%

Schlagwörter

DeutschEnglisch
Biologische Ressourcenbiological resources
Optimierungoptimization
Kontrollecontrol
Verteilte Systemedistributed systems
Heterogenitätheterogeneity
Endogenes Wachstumendogenous economic growth

Publikationen