Control of Heterogenous Systems

Heterogeneous dynamic systems provide a tool for modeling the behavior of varieties of interacting agents, having qualitatively similar description, depending, however, on some parameters that are specific for each agent. Such models arose first in population studies, where the heterogeneity of the individuals with respect to age plays a crucial role in the dynamics. On the other hand, the "vintage" economic models taking into account the age- heterogeneity of the capital stock form an important part of the modern economic growth theory, addressing issues such as investment volatility, equipment replacement, technological progress, labor allocation, etc., all in dynamic optimization framework. For example, the understanding of the anticipation effects (established in our earlier papers), which slow down the adoption of new technologies due to the perspective that even better technologies will appear in the future, requires involvement of vintage dynamic optimization models, and the profound study of these effects is one of the aims of the project. The dynamic interaction between a heterogeneous capital stock and a heterogeneous human population raised several challenging directions of research in the population economics. In view of the considerable ageing of the population in many European countries it is of particular interest to investigate the intertemporal consequences (in terms of utility) of the present age structure of the population, taking into account possible changes in savings rates, migration, pension age, international debts, etc. We recently carried out a restricted version of such an investigation with Austrian data. The new numerical approaches for heterogeneous systems that the project is aimed to develop will allow for a substantial extension of this study. Although the theory of age-structured dynamic systems is developed in many important aspects, the intertemporal optimization of such systems is not studied systematically. The main goal of the project is to develop the necessary tools for analytic and advanced numerical investigation of heterogeneous dynamic optimization models. These tools will be applied to the above mentioned problems and will provide new insights into the capital growth theory and the population economics. Heterogeneous systems are of crucial importance also in epidemiology. Along with age, also other types of heterogeneity can be essential in the dynamics of an infectious disease: quality of the immune system, frailty, exposition to risk, etc. These are also incorporated in the general framework of heterogeneous systems that the project is aimed to develop.

Heterogeneous dynamic systems provide a tool for modeling the behavior of varieties of interacting agents, having qualitatively similar description, depending, however, on some parameters that are specific for each agent. Such models arose first in population studies, where the heterogeneity of the individuals with respect to age plays a crucial role in the dynamics. On the other hand, the "vintage" economic models taking into account the age- heterogeneity of the capital stock form an important part of the modern economic growth theory, addressing issues such as investment volatility, equipment replacement, technological progress, labor allocation, etc., all in dynamic optimization framework. For example, the understanding of the anticipation effects (established in our earlier papers), which slow down the adoption of new technologies due to the perspective that even better technologies will appear in the future, requires involvement of vintage dynamic optimization models, and the profound study of these effects is one of the aims of the project. The dynamic interaction between a heterogeneous capital stock and a heterogeneous human population raised several challenging directions of research in the population economics. In view of the considerable ageing of the population in many European countries it is of particular interest to investigate the intertemporal consequences (in terms of utility) of the present age structure of the population, taking into account possible changes in savings rates, migration, pension age, international debts, etc. We recently carried out a restricted version of such an investigation with Austrian data. The new numerical approaches for heterogeneous systems that the project is aimed to develop will allow for a substantial extension of this study. Although the theory of age-structured dynamic systems is developed in many important aspects, the intertemporal optimization of such systems is not studied systematically. The main goal of the project is to develop the necessary tools for analytic and advanced numerical investigation of heterogeneous dynamic optimization models. These tools will be applied to the above mentioned problems and will provide new insights into the capital growth theory and the population economics. Heterogeneous systems are of crucial importance also in epidemiology. Along with age, also other types of heterogeneity can be essential in the dynamics of an infectious disease: quality of the immune system, frailty, exposition to risk, etc. These are also incorporated in the general framework of heterogeneous systems that the project is aimed to develop.