Koç University, Mathematics Seminar

Date & Time: Thursday, April 7, 16:00-17:00

Place: SCI 129

Speaker: Gabor Rudolf (Koç University)

Title: Stochastic dominance relations and duality

Abstract: In this talk we first discuss stochastic dominance relations and their use in optimization problems, focusing on the well-known key result that Lagrangian dual solutions correspond to utility functions. Based on an alternative equivalent definition of the dominance relation we develop a formulation where dual solutions interpreted as coherent risk measures. This approach can be extended to multiobjective decision problems featuring multivariate dominance constraints. We generalize existing duality results and discuss an important connection to a well-known theorem of Strassen on the existence of measures on product spaces with given marginals. For discrete measure spaces Strassen's theorem becomes a special case of the combinatorial Max-Flow-Min-Cut theorem; we show that using appropriate strong duality results and discretization techniques Strassen's result can be derived from its elementary discrete counterpart, and establish a general framework that connects combinatorial dual-integrality results to analogous statements for general measure spaces.

Speaker's Homepage: http://home.ku.edu.tr/~grudolf/