Mathematical Economics has sprung from the outgrowth of Applied Mathematics in economic models and aims at the construction of a rigorous and unified Economic Theory.
Techniques of Functional Analysis, Topology, and Differential Topology are of ample use in the central economic model: The Theory of General Equilibrium. Differential Equations and Dynamical Systems furnish mathematical economists with basic tools for process analysis or economic dynamics. Probability is fundamental to the study of economic models where risk and uncertainly are present.
Allied to Mathematical Economics is Econometrics, which is the study of the properties of data generation processes, techniques of economic data analysis and methods of test evaluation of economic hypotheses. In this field the tools developed by Statistics are of central importance.
The main fields of research studies currently being conducted at IMPA are:
- General Equilibrium
- Information and Uncertainty Economics
- Incomplete Markets
- Dynamic Programming and Capital Theory
- Capital Theory
- Dynamical Programming