• SIGMAOPT SEMINAR
  • Speaker: Andreas Hamel, Department of Operations Research and Financial Engineering, Princeton University
  • Title: The Fundamental Duality Formula in Set-Valued Optimization
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Access Grid Venue: UniSA
  • Time and Date: 11:30 am, Fri, 27th 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 set-valued 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 set-valued risk measures, a cutting edge development in mathematical finance. It turns out that the proposed duality theory for set-valued functions provides a satisfying framework not only for set-valued risk measures, but also for no-arbitrage and superhedging theorems in conical market models.

  • Download: Lecture notes (110 KB)

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