 SIGMAOPT SEMINAR
 Speaker: Andreas Hamel, Department of Operations Research and Financial Engineering, Princeton University
 Title: The Fundamental Duality Formula in SetValued Optimization
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UniSA
 Time and Date: 11:30 am, Fri, 27^{th} Aug 2010
 (11:00 am Adelaide time.)
 Abstract:
The fundamental duality formula (see Zalinescu ”Convex Analysis in General Vector Spaces”, Theorem 2.7.1) is extended to functions mapping into the power set of a topological linear space with a convex cone which is not necessarily pointed. Pairs of linear functionals are used as dual variables instead of linear operators. The talk will consist of three parts. First, motivations and explanations are given for the infimum approach to setvalued optimization. It deviates from other approaches, and it seems to be the only way to obtain a theory which completely resembles the scalar case. In the second part, the main results are presented, namely the fundamental duality formula and several conclusions. The third part deals with duality formulas for setvalued risk measures, a cutting edge development in mathematical finance. It turns out that the proposed duality theory for setvalued functions provides a satisfying framework not only for setvalued risk measures, but also for noarbitrage and superhedging theorems in conical market models.
 Download: Lecture notes (110 KB)
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