Set Optimization and Applications - The State of the Art: From Set Relations to Set-Valued Risk Measures

ISBN-13: 9783662511398 / Angielski / Miękka / 2016 / 331 str.

Andreas H. Hamel; Frank Heyde; Andreas Lohne

Spis treści

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 respect

to random partial orders.- Generalized minimality in set optimization.- On characterization of Nash equilibrium strategy in bi

matrix games with set payos.

Blurb

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.