Set Optimization and Applications - The State of the Art

This volume presents five surveys with extensive
bibliographies and six original contributions on set optimization and its applications
in mathematical finance and game theory. The topics range from more
conventional approaches that look for minimal/maximal elements with respect to
vector orders or set relations, to the new complete-lattice approach that
comprises a coherent solution concept for set optimization problems, along with
existence results, duality theorems, optimality conditions, variational
inequalities and theoretical foundations for algorithms. Modern approaches to
scalarization methods can be found as well as a fundamental contribution to conditional
analysis. The theory is tailor-made for financial applications, in particular risk
evaluation and [super-]hedging for market models with transaction costs, but it
also provides a refreshing new perspective on vector optimization. There is no
comparable volume on the market, making the book an invaluable resource for
researchers working in vector optimization and multi-criteria decision-making, mathematical
finance and economics as well as [set-valued] variational analysis.