This project aims to develop and apply mathematical analysis, and in particular nonstandard analysis, to economic modeling.

Nonstandard analysis models infinitely large and infinitely small quantities (infinitesimals) in a logically consistent way. This often yields a simpler framework for models than the classical framework, which often requires quite some theoretical mathematical constructions (e.g., measures on infinite product spaces as a framework for stochastic processes). Initially, we will pursue research in functional analysis, which provides a.o. a framework for solutions to partial differential equations.

We want to develop models for contemporary economic problems related to sustainability that take into account the finite nature of natural resources, such as macroeconomic models in ecological economics, models of energy impact, models of economic inequality, models of the impact of monetary systems, ...