A hacking day of Mathematics for Data Science at the Department of Mathematics

Andreas Hamel (Courtesy by the press office of Free University of Bozen)

Andreas Hamel
Faculty of Economics and Management
Free University of Bozen-Bolzano
website
Bio PhD in 1996 and German "Habilitation" in 2005, both in Mathematics, at Martin Luther University Halle-Wittenberg, Germany. Taught math and math related courses at University Halle-Wittenberg (Germany), IMPA, Rio de Janeiro (Brazil), Princeton University (USA) and Yeshiva University New York (USA), among them one of the first ever courses on "Convex Analysis and Financial Risk Measures" in 2003. Co-developed new area "Set Optimization" with surprising applications in mathematical finance, economics, statistics, game theory and multi-criteria decision making; invented set optimization approach to risk measures for multivariate positions and to multivariate quantiles. These are two links with more information:

Syllabus

Many relatively straightforward mathematical concepts become questionable or even dubious when naively transferred from the real-valued to the multi-criteria case, i.e., to more than one objective function. A few examples: (1) What can you say about linear programming duality for multi-criteria problems? (ask your OR/optimization prof) (2) What is the quantile, e.g., the median, of a multivariate random variable? (ask your statistics prof) (3) Do the worst-case and best-response strategies for two-person zero-sum games still coincide if the payoff is not one, but higher dimensional? (ask your game theory prof) (4) How do you do multi-utility maximization, i.e., find best elements for a non-total preference relation which can only be represented by a (maybe infinite) family of real-valued functions and not a single one? (ask you econ profs) (5) A little more technical, but very fundamental: what is the Legendre-Fenchel transform/conjugate of a vector- or even set-valued function? (ask your physics/calculus of variations/analysis prof) In this lecture, it is shown that the so-called complete-lattice approach to set optimization (yes, we start with some basics from order and lattice theory) provides new and exiting answers to the above and many more questions in a very textbook-like manner.

References

  1. A survey: Hamel AH, Heyde F, Loehne A, Rudloff B, Schrage C, Set optimization-a rather short introduction. In: Hamel, A.H., Heyde, F., Loehne, A., Rudloff, B., Schrage, C. (eds.), Set optimization and applications - the state of the art. From set relations to set-valued risk measures, Springer-Verlag Berlin 2015, pp. 65-141
  2. Game theory: A.H. Hamel, A. Loehne, A set optimization approach to zero-sum matrix games with multi-dimensional payoffs, Math. Methods Oper. Res., 88(3), 69-397, 2018
  3. Multi-utility maximization: A.H. Hamel, Q.Q. Wang, A set optimisation approach to utility maximisation under transaction costs, Decisions in Economics and Finance 40(1-2), 257-275, 2017
  4. Statistics: A.H. Hamel, D. Kostner, Cone distribution functions and quantiles for multivariate random variables, J. Multivariate Analysis 167, 97-113, 2018
  5. Multivariate risk measures: A.H. Hamel, F. Heyde, Duality for set-valued measures of risk, SIAM J Financial Math. 1(1), 66-95, 2010
  6. Convex analysis for set-valued functions: A.H. Hamel, A duality theory for set-valued functions I: Fenchel conjugation theory, Set-Valued Variational Analysis 17(2), 153-182, 2009

Schedule

  • 21 February 2020, 14:30-18:30 @ A224 Povo 1

Details

  • Poster: PDF
  • The participation is free. Please send an email to Prof. Claudio Agostinelli.
  • For further information, please contact Prof. Claudio Agostinelli
  • Venue: Polo Scientifico e Tecnologico F. Ferrari
  • Language: English
  • The photo of Andreas Hamel is courtesy by the press office of Free University of Bozen-Bolzano

Material (Restricted access, user: SO2020)