04166nam a22005535i 4500 978-3-031-57988-2 DE-He213 20251030112343.0 cr nn 008mamaa 240630s2024 sz | s |||| 0|eng d 9783031579882 978-3-031-57988-2 10.1007/978-3-031-57988-2 doi QA402.5-402.6 PBU bicssc MAT042000 bisacsh PBU thema Dentcheva, Darinka. author. aut http://id.loc.gov/vocabulary/relators/aut 79672 Risk-Averse Optimization and Control [electronic resource] : Theory and Methods / by Darinka Dentcheva, Andrzej Ruszczyński. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XV, 451 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Springer Series in Operations Research and Financial Engineering, 2197-1773 Elements of the Utility Theory -- Measures of Risk -- Optimization of Measures of Risk -- Dynamic Risk Optimization -- Optimization with Stochastic Dominance Constraints -- Multivariate and Sequential Stochastic Orders -- Numerical Methods for Problems with Stochastic Dominance Constraints -- Risk-Averse Control of Markov Systems. This book offers a comprehensive presentation of the theory and methods of risk-averse optimization and control. Problems of this type arise in finance, energy production and distribution, supply chain management, medicine, and many other areas, where not only the average performance of a stochastic system is essential, but also high-impact and low-probability events must be taken into account. The book is a self-contained presentation of the utility theory, the theory of measures of risk, including systemic and dynamic measures of risk, and their use in optimization and control models. It also covers stochastic dominance relations and their application as constraints in optimization models. Optimality conditions for problems with nondifferentiable and nonconvex functions and operators involving risk measures and stochastic dominance relations are discussed. Much attention is paid to multi-stage risk-averse optimization problems and to risk-averse Markov decision problems. Specialized algorithms for solving risk-averse optimization and control problems are presented and analyzed: stochastic subgradient methods for risk optimization, decomposition methods for dynamic problems, event cut and dual methods for stochastic dominance constraints, and policy iteration methods for control problems. The target audience is researchers and graduate students in the areas of mathematics, business analytics, insurance and finance, engineering, and computer science. The theoretical considerations are illustrated with examples, which make the book useful material for advanced courses in the area. . Mathematical optimization. 65522 Social sciences Mathematics. 69736 Mathematics. 65523 Optimization. 65528 Mathematics in Business, Economics and Finance. 69739 Mathematics. 65523 Ruszczyński, Andrzej. author. (orcid)0000-0002-4571-1469 https://orcid.org/0000-0002-4571-1469 aut http://id.loc.gov/vocabulary/relators/aut 79673 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031579875 Printed edition: 9783031579899 Printed edition: 9783031579905 Springer Series in Operations Research and Financial Engineering, 2197-1773 76963 https://doi.org/10.1007/978-3-031-57988-2 ZDB-2-SMA ZDB-2-SXMS 61180 61180