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Free University of Bozen-Bolzano

Quantitative Methods and Economic Modeling

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Coordinator

Mirco Tonin

Members

Paolo Coletti, Francesca Marta Lilja Di Lascio, Alessandro Fedele, Enrico Foscolo, Andreas Heinrich Hamel, Yuriy Kaniovskyi, Francesco Ravazzolo, Steven Eric Stillman, Carola Schrage, Stefan Franz Schubert, Alex Weissensteiner.

Description

The Research Cluster encompasses research in the theoretical foundation and the methodological aspects that are relevant for the empirical study of the economy/economic life/economics.

Its research activities can be classified into to the following interconnected domains:

  • Growth, regional development and business cycles.
  • Labour economics, public finance and evaluation of public policies.
  • International Economics and Macroeconomics modelling.
  • Mathematical and numerical methods (decision theory, risk analysis, optimization) of economics, finance and management science and their theoretical foundations.
  • Statistical methods and Econometrics, including computational statistic and Monte-Carlo simulations, data analysis and forecasting methods, big data sets and high-dimensional models, classification and network analysis.

Involving experts in methodology as well as applied scientists, the research agenda addresses issues that are at the core of the current scientific debate, affecting society, individuals, institutions and markets.

Highlight

An abstract convexity approach to scalarization in set/vector optimization and to multi-utility representation

Researcher at unibz

Andreas Hamel

External Collaborators

Giovanni Crespi, Matteo Rocca, Fabian Flores-Bazan

Description of the Project

'Economics needs a scientific revolution.' (J.-P. Bouchaud in nature, Oct. 2008). What could mathematics contribute?

In the overwhelming majority of publications in mathematical economics and mathematical finance it is assumed that economic agents (consumers, producers, traders, even regulators) have total preferences for the objects they deal with. Which means that lotteries, portfolios, commodity bundles, assets and liabilities (random or not random) can be ranked in the same way as real numbers: one can always say which of two numbers is greater than or equal to the other.

In the research project the following hypothesis are discussed:

  • all rankings are wrong,
  • (market) equilibria do not exist,
  • liquidation matters,
  • going set-valued helps,
  • optimal decisions can be made even without (total) rankings.

Specifically, the project aims at developing a new axiomatic framework for a “new” mathematics for economics, following the set optimization approach presented in:

A.H. Hamel, F. Heyde, A. Loehne, B. Rudloff and C. Schrage (editors), Set Optimization and Applications - The State of the Art, Springer-Verlag, Proceedings in Mathematics and Statistics 151, 2015.

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