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Free University of Bozen-Bolzano

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Tenured full professors | Mathematics

Andreas Heinrich Hamel

Andreas.Hamel@unibz.it

+39 0474 013651

BK A1.11
Faculty of Economics and Management
Universitätsplatz 1 - Piazzetta dell'Università, 1
39031
Bruneck-Brunico
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Curriculum Vitae

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Short bio

Taught math and math related courses at University Halle-Wittenberg (Germany), IMPA, Rio de Janeiro (Brazil), Princeton University and Yeshiva University New York (USA).

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.

Research Focuses


Convex and variational analysis; optimization theory, in particular problems with a set-valued objective; mathematical finance, in particular market models with transaction costs; mathematical economics, in particular incomplete preferences and game theory; multivariate statistics, in particular quantiles. 

Research Macro Area

Data Science and Mathematical Methods

Info

Upcoming Workshop "Set Optimization and Statistics" at Free University of Bozen-Bolzano, Italy, Nov. 21-22, 2019.
 

Selected publications

A.H. Hamel, F. Heyde, B. Rudloff, Set-valued risk measures for conical market models, Math. Financial Economics 5(1), 1-28, 2011
Q.H. Ansari, A.H. Hamel, P.K. Sharma, Ekeland’s variational principle with weighted set order relations, Math. Methods. Oper. Res., online first, 2019
A.H. Hamel, An epsilon-Lagrange multiplier rule for a mathematical programming problem on a Banach space, Optimization 49, 137-149, 2001
A.H. Hamel, Phelps’ lemma, Danes’ drop theorem and Ekeland’s principle in locally convex spaces, Proc. Amer. Math. Soc. 131, 3025–3038, 2003
A.H. Hamel, F. Heyde, A. Löhne, C. Tammer, K. Winkler, Closing the duality gap in linear vector optimization, J. Convex Anal. 11(1), 163-178, 2004
A.H. Hamel, A. Loehne, Equivalents to Ekeland's variational principle in uniform spaces, Norlin. Anal. 62(5), 913-924, 2005
A.H. Hamel, A. Loehne, Minimal element theorems and Ekeland's principle with set relations, J. Nonlin. Convex Anal. 7(1), 19-37, 2006
A.H. Hamel, C. Tammer, Minimal elements for product orders, Optimization 57(2), 263-275, 2008
A.H. Hamel, A duality theory for set-valued functions I: Fenchel conjugation theory, Set-Valued Variational Analysis 17(2), 153-182, 2009
A.H. Hamel, F. Heyde, Duality for set-valued measures of risk, SIAM J Financial Math. 1(1), 66-95, 2010
A.H. Hamel, A Fenchel-Rockafellar duality theorem for set-valued optimization, Optimization 60(8-9), 1023-1043, 2011
A.H. Hamel, D. Kostner, Cone distribution functions and quantiles for multivariate random variables, J. Multivariate Analysis 167, 97-113, 2018
A.H. Hamel, C. Schrage, Notes on extended real- and set-valued functions, J. Convex Analysis, 19(2), 355-384, 2012
A.H. Hamel, B. Rudloff, M. Yankova, Set-valued average value at risk and its computation, Math. Financial Economics 7(2), 229-246, 2013
A.H. Hamel, A. Loehne, B. Rudloff, Benson type algorithms for linear vector optimization and applications, J. Global Optimization 59(4), 811-836, 2014
A.H. Hamel, A. Loehne, Lagrange duality in set optimization, J. Optim. Theory Appl. 161(2), 368-397, 2014
A.H. Hamel, C. Schrage, Directional Derivatives, Subdifferentials and Optimality Conditions for Set-Valued Convex Functions, Pacific J. Optimization 10(4), 667-689, 2014
G. Crespi, A.H. Hamel, C. Schrage, A Minty Variational Principle for Set-Valued Optimization, J. Math. Anal. Appl. 423(1), 770-796, 2015
S. Drapeau, A.H. Hamel, M. Kupper, Complete duality theory for quasi convex and convex set-valued functions, Set-Valued and Variational Analysis 24(2), 253-275, 2016
C. Ararat, A.H. Hamel, B. Rudloff, Set-valued shortfall and divergence risk measures, Intern. J. Theoretical and Applied Finance 20(5), 48pp., 2017
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
A.H. Hamel, A. Loehne, A set optimization approach to zero-sum matrix games with multi-dimensional payoffs, Math. Methods Oper. Res., online first, 2018
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