By Andreas H. Hamel,Frank Heyde,Andreas Löhne,Birgit Rudloff,Carola Schrage

This quantity offers 5 surveys with extensive
bibliographies and 6 unique contributions on set optimization and its applications
in mathematical finance and video game conception. the themes variety from more
conventional methods that search for minimal/maximal components with admire to
vector orders or set kinfolk, to the hot complete-lattice procedure that
comprises a coherent answer notion for set optimization difficulties, alongside with
existence effects, duality theorems, optimality stipulations, variational
inequalities and theoretical foundations for algorithms. sleek ways to
scalarization equipment are available in addition to a primary contribution to conditional
analysis. the speculation is tailored for monetary purposes, particularly risk
evaluation and [super-]hedging for marketplace types with transaction expenditures, yet it
also presents a fresh new viewpoint on vector optimization. there's no
comparable quantity out there, making the booklet a useful source for
researchers operating in vector optimization and multi-criteria decision-making, mathematical
finance and economics in addition to [set-valued] variational analysis.


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