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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.
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.
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