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This volume presents five surveys with extensivebibliographies and six original contributions on set optimization and its applicationsin mathematical finance and game theory. The topics range from moreconventional approaches that look for minimal/maximal elements with respect tovector orders or set relations, to the new complete-lattice approach thatcomprises a coherent solution concept for set optimization problems, along withexistence results, duality theorems, optimality conditions, variationalinequalities and theoretical foundations for algorithms. Modern approaches toscalarization methods can be found as well as a fundamental contribution to conditionalanalysis. The theory is tailor-made for financial applications, in particular riskevaluation and [super-]hedging for market models with transaction costs, but italso provides a refreshing new perspective on vector optimization. There is nocomparable volume on the market, making the book an invaluable resource forresearchers working in vector optimization and multi-criteria decision-making, mathematicalfinance and economics as well as [set-valued] variational analysis.
List of contents
I. Surveys.- A comparison of techniques for dynamic mul-tivariate risk measures.- Nonlinear scalarization of set optimization problems with set orderings.- Set optimization - a rather short introduction.- A survey of set optimization problems with set solutions.- Linear vector optimization and European option pricing under proportional transaction costs.- II. Special topics.- Conditional analysis on Rd.- Set optimization meets variational inequalities.- Estimate of error bounds for some sets of efficient solutions of a set-valued optimization problem.- On supremal and maximal sets with respectto random partial orders.- Generalized minimality in set optimization.- On characterization of Nash equilibrium strategy in bimatrix games with set payos.
Summary
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.
