Set Optimization And Applications - The State Of The Art: From Set Relations To Set-valued Risk Measures (springer Proceedings In Mathematics & Statistics)
by Andreas Löhne /
2015 / English / PDF
4 MB Download
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.
