Risk-Averse Optimization and Control: Theory and Methods
Dentcheva, Darinka, Ruszczyński, Andrzej
- 出版商: Springer
- 出版日期: 2024-06-30
- 售價: $5,390
- 貴賓價: 9.5 折 $5,121
- 語言: 英文
- 頁數: 451
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3031579879
- ISBN-13: 9783031579875
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商品描述
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.
商品描述(中文翻譯)
本書全面介紹了風險厭惡優化和控制的理論和方法。這類問題在金融、能源生產和分配、供應鏈管理、醫學等許多領域中出現,其中不僅需要考慮隨機系統的平均性能,還需要考慮高影響和低概率事件。本書是對效用理論、風險度量理論(包括系統性和動態風險度量)以及它們在優化和控制模型中的應用的自成體系的介紹。它還涵蓋了隨機優勢關係及其在優化模型中的應用作為約束條件。討論了涉及風險度量和隨機優勢關係的非可微和非凸函數和算子的最優性條件。對多階段風險厭惡優化問題和風險厭惡馬爾可夫決策問題給予了很大的關注。
本書介紹和分析了解決風險厭惡優化和控制問題的專門算法:風險優化的隨機次梯度方法、動態問題的分解方法、隨機優勢約束的事件切割和對偶方法,以及控制問題的策略迭代方法。
目標讀者是數學、商業分析、保險和金融、工程和計算機科學領域的研究人員和研究生。理論考慮通過示例加以說明,使本書成為該領域高級課程的有用教材。