The research objectives of the project consist in exploring a new, realistic and parsimonious framework for modeling heterogeneity in economics and in investigating its implications for analyzing the volatility of financial assets. First, in order to develop this framework, a novel approach in economics is proposed based on measure-valued stochastic processes, which are extensively employed in mathematical biology to study the heterogeneity of a population with respect to a genetic characteristic. The new modeling framework is extremely relevant in the current context of increasing interest in analyzing heterogeneity effects in economics and in studying the complexity of economic systems. Second, the new framework for heterogeneity is employed to develop a micro-founded stochastic volatility model. Since the resulting continuous-time model is expected to be non-affine and endogenous, it will address some of the limitations of the existing exogenous and affine stochastic volatility models. By its own nature, the research project has a strong inter-disciplinary character, being at the intersection between finance, economics, and mathematics. The proposed methodology for modeling heterogeneity in economics is based on infinite-dimensional mathematical objects. Therefore, understanding and applying such a methodology requires mastering advanced methods from functional analysis, a branch of mathematics that deals with infinite-dimensional spaces. The project will be implemented under the supervision of an expert with vast experience both in functional analysis and in quantitative finance and with an extensive research network in both fields. The training is concerned with both scientific and professional skills. The objectives of the scientific training consist mainly in instructing the fellow with respect to the advanced tools needed during the research activities and those of the professional training in cultivating crucial transferable skills in an academic context.
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