Dynamic Optimization Under Uncertainty

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Dynamic Stochastic Optimization

Author : Kurt Marti
Publisher : Springer Science & Business Media
ISBN 13 : 3642558844
Total Pages : 337 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Dynamic Stochastic Optimization by : Kurt Marti

Download or read book Dynamic Stochastic Optimization written by Kurt Marti and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for precise evaluations and, as a result, the lack of proper management (control) may create significant risks. In order to develop robust strategies we need approaches which explic itly deal with uncertainties, risks and changing conditions. One rather general approach is to characterize (explicitly or implicitly) uncertainties by objec tive or subjective probabilities (measures of confidence or belief). This leads us to stochastic optimization problems which can rarely be solved by using the standard deterministic optimization and optimal control methods. In the stochastic optimization the accent is on problems with a large number of deci sion and random variables, and consequently the focus ofattention is directed to efficient solution procedures rather than to (analytical) closed-form solu tions. Objective and constraint functions of dynamic stochastic optimization problems have the form of multidimensional integrals of rather involved in that may have a nonsmooth and even discontinuous character - the tegrands typical situation for "hit-or-miss" type of decision making problems involving irreversibility ofdecisions or/and abrupt changes ofthe system. In general, the exact evaluation of such functions (as is assumed in the standard optimization and control theory) is practically impossible. Also, the problem does not often possess the separability properties that allow to derive the standard in control theory recursive (Bellman) equations.

Decision Making under Uncertainty in Financial Markets

Author : Jonas Ekblom
Publisher : Linköping University Electronic Press
ISBN 13 : 9176852024
Total Pages : 36 pages
Book Rating : 4.1/5 (768 download)

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Book Synopsis Decision Making under Uncertainty in Financial Markets by : Jonas Ekblom

Download or read book Decision Making under Uncertainty in Financial Markets written by Jonas Ekblom and published by Linköping University Electronic Press. This book was released on 2018-09-13 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis addresses the topic of decision making under uncertainty, with particular focus on financial markets. The aim of this research is to support improved decisions in practice, and related to this, to advance our understanding of financial markets. Stochastic optimization provides the tools to determine optimal decisions in uncertain environments, and the optimality conditions of these models produce insights into how financial markets work. To be more concrete, a great deal of financial theory is based on optimality conditions derived from stochastic optimization models. Therefore, an important part of the development of financial theory is to study stochastic optimization models that step-by-step better capture the essence of reality. This is the motivation behind the focus of this thesis, which is to study methods that in relation to prevailing models that underlie financial theory allow additional real-world complexities to be properly modeled. The overall purpose of this thesis is to develop and evaluate stochastic optimization models that support improved decisions under uncertainty on financial markets. The research into stochastic optimization in financial literature has traditionally focused on problem formulations that allow closed-form or `exact' numerical solutions; typically through the application of dynamic programming or optimal control. The focus in this thesis is on two other optimization methods, namely stochastic programming and approximate dynamic programming, which open up opportunities to study new classes of financial problems. More specifically, these optimization methods allow additional and important aspects of many real-world problems to be captured. This thesis contributes with several insights that are relevant for both financial and stochastic optimization literature. First, we show that the modeling of several real-world aspects traditionally not considered in the literature are important components in a model which supports corporate hedging decisions. Specifically, we document the importance of modeling term premia, a rich asset universe and transaction costs. Secondly, we provide two methodological contributions to the stochastic programming literature by: (i) highlighting the challenges of realizing improved decisions through more stages in stochastic programming models; and (ii) developing an importance sampling method that can be used to produce high solution quality with few scenarios. Finally, we design an approximate dynamic programming model that gives close to optimal solutions to the classic, and thus far unsolved, portfolio choice problem with constant relative risk aversion preferences and transaction costs, given many risky assets and a large number of time periods.

Optimization Techniques for Problem Solving in Uncertainty

Author : Tilahun, Surafel Luleseged
Publisher : IGI Global
ISBN 13 : 1522550925
Total Pages : 313 pages
Book Rating : 4.5/5 (225 download)

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Book Synopsis Optimization Techniques for Problem Solving in Uncertainty by : Tilahun, Surafel Luleseged

Download or read book Optimization Techniques for Problem Solving in Uncertainty written by Tilahun, Surafel Luleseged and published by IGI Global. This book was released on 2018-06-22 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: When it comes to optimization techniques, in some cases, the available information from real models may not be enough to construct either a probability distribution or a membership function for problem solving. In such cases, there are various theories that can be used to quantify the uncertain aspects. Optimization Techniques for Problem Solving in Uncertainty is a scholarly reference resource that looks at uncertain aspects involved in different disciplines and applications. Featuring coverage on a wide range of topics including uncertain preference, fuzzy multilevel programming, and metaheuristic applications, this book is geared towards engineers, managers, researchers, and post-graduate students seeking emerging research in the field of optimization.

Uncertain Optimal Control

Author : Yuanguo Zhu
Publisher : Springer
ISBN 13 : 9811321345
Total Pages : 208 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Uncertain Optimal Control by : Yuanguo Zhu

Download or read book Uncertain Optimal Control written by Yuanguo Zhu and published by Springer. This book was released on 2018-08-29 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the theory and applications of uncertain optimal control, and establishes two types of models including expected value uncertain optimal control and optimistic value uncertain optimal control. These models, which have continuous-time forms and discrete-time forms, make use of dynamic programming. The uncertain optimal control theory relates to equations of optimality, uncertain bang-bang optimal control, optimal control with switched uncertain system, and optimal control for uncertain system with time-delay. Uncertain optimal control has applications in portfolio selection, engineering, and games. The book is a useful resource for researchers, engineers, and students in the fields of mathematics, cybernetics, operations research, industrial engineering, artificial intelligence, economics, and management science.

Robust Optimization

Author : Aharon Ben-Tal
Publisher : Princeton University Press
ISBN 13 : 1400831059
Total Pages : 576 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Robust Optimization by : Aharon Ben-Tal

Download or read book Robust Optimization written by Aharon Ben-Tal and published by Princeton University Press. This book was released on 2009-08-10 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject.

Optimization Under Uncertainty with Applications to Aerospace Engineering

Author : Massimiliano Vasile
Publisher : Springer Nature
ISBN 13 : 3030601668
Total Pages : 573 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Optimization Under Uncertainty with Applications to Aerospace Engineering by : Massimiliano Vasile

Download or read book Optimization Under Uncertainty with Applications to Aerospace Engineering written by Massimiliano Vasile and published by Springer Nature. This book was released on 2021-02-15 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an expanding world with limited resources, optimization and uncertainty quantification have become a necessity when handling complex systems and processes. This book provides the foundational material necessary for those who wish to embark on advanced research at the limits of computability, collecting together lecture material from leading experts across the topics of optimization, uncertainty quantification and aerospace engineering. The aerospace sector in particular has stringent performance requirements on highly complex systems, for which solutions are expected to be optimal and reliable at the same time. The text covers a wide range of techniques and methods, from polynomial chaos expansions for uncertainty quantification to Bayesian and Imprecise Probability theories, and from Markov chains to surrogate models based on Gaussian processes. The book will serve as a valuable tool for practitioners, researchers and PhD students.

Hybrid Offline/Online Methods for Optimization Under Uncertainty

Author : A. De Filippo
Publisher : IOS Press
ISBN 13 : 1643682636
Total Pages : 126 pages
Book Rating : 4.6/5 (436 download)

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Book Synopsis Hybrid Offline/Online Methods for Optimization Under Uncertainty by : A. De Filippo

Download or read book Hybrid Offline/Online Methods for Optimization Under Uncertainty written by A. De Filippo and published by IOS Press. This book was released on 2022-04-12 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Balancing the solution-quality/time trade-off and optimizing problems which feature offline and online phases can deliver significant improvements in efficiency and budget control. Offline/online integration yields benefits by achieving high quality solutions while reducing online computation time. This book considers multi-stage optimization problems under uncertainty and proposes various methods that have broad applicability. Due to the complexity of the task, the most popular approaches depend on the temporal granularity of the decisions to be made and are, in general, sampling-based methods and heuristics. Long-term strategic decisions that may have a major impact are typically solved using these more accurate, but expensive, sampling-based approaches. Short-term operational decisions often need to be made over multiple steps within a short time frame and are commonly addressed via polynomial-time heuristics, with the more advanced sampling-based methods only being applicable if their computational cost can be carefully managed. Despite being strongly interconnected, these 2 phases are typically solved in isolation. In the first part of the book, general methods based on a tighter integration between the two phases are proposed and their applicability explored, and these may lead to significant improvements. The second part of the book focuses on how to manage the cost/quality trade-off of online stochastic anticipatory algorithms, taking advantage of some offline information. All the methods proposed here provide multiple options to balance the quality/time trade-off in optimization problems that involve offline and online phases, and are suitable for a variety of practical application scenarios.

Dynamic Economics

Author : Gregory C. Chow
Publisher : Oxford University Press
ISBN 13 : 0195356314
Total Pages : 249 pages
Book Rating : 4.1/5 (953 download)

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Book Synopsis Dynamic Economics by : Gregory C. Chow

Download or read book Dynamic Economics written by Gregory C. Chow and published by Oxford University Press. This book was released on 1997-02-13 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work provides a unified and simple treatment of dynamic economics using dynamic optimization as the main theme, and the method of Lagrange multipliers to solve dynamic economic problems. The author presents the optimization framework for dynamic economics in order that readers can understand the approach and use it as they see fit. Instead of using dynamic programming, the author chooses instead to use the method of Lagrange multipliers in the analysis of dynamic optimization because it is easier and more efficient than dynamic programming, and allows readers to understand the substance of dynamic economics better. The author treats a number of topics in economics, including economic growth, macroeconomics, microeconomics, finance and dynamic games. The book also teaches by examples, using concepts to solve simple problems; it then moves to general propositions.

Essays on Financial Dynamic Optimization Under Uncertainty

Author : Gerhard Hambusch
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (951 download)

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Book Synopsis Essays on Financial Dynamic Optimization Under Uncertainty by : Gerhard Hambusch

Download or read book Essays on Financial Dynamic Optimization Under Uncertainty written by Gerhard Hambusch and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dynamic Optimization Under Uncertainty

Author : Peter Jason Kalman
Publisher :
ISBN 13 :
Total Pages : 44 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Dynamic Optimization Under Uncertainty by : Peter Jason Kalman

Download or read book Dynamic Optimization Under Uncertainty written by Peter Jason Kalman and published by . This book was released on 1974 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advances in Uncertainty Quantification and Optimization Under Uncertainty with Aerospace Applications

Author : Massimiliano Vasile
Publisher : Springer Nature
ISBN 13 : 3030805425
Total Pages : 448 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Advances in Uncertainty Quantification and Optimization Under Uncertainty with Aerospace Applications by : Massimiliano Vasile

Download or read book Advances in Uncertainty Quantification and Optimization Under Uncertainty with Aerospace Applications written by Massimiliano Vasile and published by Springer Nature. This book was released on 2022-01-27 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2020 International Conference on Uncertainty Quantification & Optimization gathered together internationally renowned researchers in the fields of optimization and uncertainty quantification. The resulting proceedings cover all related aspects of computational uncertainty management and optimization, with particular emphasis on aerospace engineering problems. The book contributions are organized under four major themes: Applications of Uncertainty in Aerospace & Engineering Imprecise Probability, Theory and Applications Robust and Reliability-Based Design Optimisation in Aerospace Engineering Uncertainty Quantification, Identification and Calibration in Aerospace Models This proceedings volume is useful across disciplines, as it brings the expertise of theoretical and application researchers together in a unified framework.

Reinforcement Learning and Stochastic Optimization

Author : Warren B. Powell
Publisher : John Wiley & Sons
ISBN 13 : 1119815037
Total Pages : 1090 pages
Book Rating : 4.1/5 (198 download)

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Book Synopsis Reinforcement Learning and Stochastic Optimization by : Warren B. Powell

Download or read book Reinforcement Learning and Stochastic Optimization written by Warren B. Powell and published by John Wiley & Sons. This book was released on 2022-03-15 with total page 1090 pages. Available in PDF, EPUB and Kindle. Book excerpt: REINFORCEMENT LEARNING AND STOCHASTIC OPTIMIZATION Clearing the jungle of stochastic optimization Sequential decision problems, which consist of “decision, information, decision, information,” are ubiquitous, spanning virtually every human activity ranging from business applications, health (personal and public health, and medical decision making), energy, the sciences, all fields of engineering, finance, and e-commerce. The diversity of applications attracted the attention of at least 15 distinct fields of research, using eight distinct notational systems which produced a vast array of analytical tools. A byproduct is that powerful tools developed in one community may be unknown to other communities. Reinforcement Learning and Stochastic Optimization offers a single canonical framework that can model any sequential decision problem using five core components: state variables, decision variables, exogenous information variables, transition function, and objective function. This book highlights twelve types of uncertainty that might enter any model and pulls together the diverse set of methods for making decisions, known as policies, into four fundamental classes that span every method suggested in the academic literature or used in practice. Reinforcement Learning and Stochastic Optimization is the first book to provide a balanced treatment of the different methods for modeling and solving sequential decision problems, following the style used by most books on machine learning, optimization, and simulation. The presentation is designed for readers with a course in probability and statistics, and an interest in modeling and applications. Linear programming is occasionally used for specific problem classes. The book is designed for readers who are new to the field, as well as those with some background in optimization under uncertainty. Throughout this book, readers will find references to over 100 different applications, spanning pure learning problems, dynamic resource allocation problems, general state-dependent problems, and hybrid learning/resource allocation problems such as those that arose in the COVID pandemic. There are 370 exercises, organized into seven groups, ranging from review questions, modeling, computation, problem solving, theory, programming exercises and a “diary problem” that a reader chooses at the beginning of the book, and which is used as a basis for questions throughout the rest of the book.

Investment under Uncertainty

Author : Robert K. Dixit
Publisher : Princeton University Press
ISBN 13 : 1400830176
Total Pages : 484 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Investment under Uncertainty by : Robert K. Dixit

Download or read book Investment under Uncertainty written by Robert K. Dixit and published by Princeton University Press. This book was released on 2012-07-14 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: How should firms decide whether and when to invest in new capital equipment, additions to their workforce, or the development of new products? Why have traditional economic models of investment failed to explain the behavior of investment spending in the United States and other countries? In this book, Avinash Dixit and Robert Pindyck provide the first detailed exposition of a new theoretical approach to the capital investment decisions of firms, stressing the irreversibility of most investment decisions, and the ongoing uncertainty of the economic environment in which these decisions are made. In so doing, they answer important questions about investment decisions and the behavior of investment spending. This new approach to investment recognizes the option value of waiting for better (but never complete) information. It exploits an analogy with the theory of options in financial markets, which permits a much richer dynamic framework than was possible with the traditional theory of investment. The authors present the new theory in a clear and systematic way, and consolidate, synthesize, and extend the various strands of research that have come out of the theory. Their book shows the importance of the theory for understanding investment behavior of firms; develops the implications of this theory for industry dynamics and for government policy concerning investment; and shows how the theory can be applied to specific industries and to a wide variety of business problems.

Assessment and Future Directions of Nonlinear Model Predictive Control

Author : Rolf Findeisen
Publisher : Springer
ISBN 13 : 3540726993
Total Pages : 644 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Assessment and Future Directions of Nonlinear Model Predictive Control by : Rolf Findeisen

Download or read book Assessment and Future Directions of Nonlinear Model Predictive Control written by Rolf Findeisen and published by Springer. This book was released on 2007-09-08 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thepastthree decadeshaveseenrapiddevelopmentin the areaofmodelpred- tive control with respect to both theoretical and application aspects. Over these 30 years, model predictive control for linear systems has been widely applied, especially in the area of process control. However, today’s applications often require driving the process over a wide region and close to the boundaries of - erability, while satisfying constraints and achieving near-optimal performance. Consequently, the application of linear control methods does not always lead to satisfactory performance, and here nonlinear methods must be employed. This is one of the reasons why nonlinear model predictive control (NMPC) has - joyed signi?cant attention over the past years,with a number of recent advances on both the theoretical and application frontier. Additionally, the widespread availability and steadily increasing power of today’s computers, as well as the development of specially tailored numerical solution methods for NMPC, bring thepracticalapplicabilityofNMPCwithinreachevenforveryfastsystems.This has led to a series of new, exciting developments, along with new challenges in the area of NMPC.

Continuous-time Stochastic Control and Optimization with Financial Applications

Author : Huyên Pham
Publisher : Springer Science & Business Media
ISBN 13 : 3540895000
Total Pages : 243 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Continuous-time Stochastic Control and Optimization with Financial Applications by : Huyên Pham

Download or read book Continuous-time Stochastic Control and Optimization with Financial Applications written by Huyên Pham and published by Springer Science & Business Media. This book was released on 2009-05-28 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.

Approximate Dynamic Programming

Author : Warren B. Powell
Publisher : John Wiley & Sons
ISBN 13 : 0470182954
Total Pages : 487 pages
Book Rating : 4.4/5 (71 download)

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Book Synopsis Approximate Dynamic Programming by : Warren B. Powell

Download or read book Approximate Dynamic Programming written by Warren B. Powell and published by John Wiley & Sons. This book was released on 2007-10-05 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete and accessible introduction to the real-world applications of approximate dynamic programming With the growing levels of sophistication in modern-day operations, it is vital for practitioners to understand how to approach, model, and solve complex industrial problems. Approximate Dynamic Programming is a result of the author's decades of experience working in large industrial settings to develop practical and high-quality solutions to problems that involve making decisions in the presence of uncertainty. This groundbreaking book uniquely integrates four distinct disciplines—Markov design processes, mathematical programming, simulation, and statistics—to demonstrate how to successfully model and solve a wide range of real-life problems using the techniques of approximate dynamic programming (ADP). The reader is introduced to the three curses of dimensionality that impact complex problems and is also shown how the post-decision state variable allows for the use of classical algorithmic strategies from operations research to treat complex stochastic optimization problems. Designed as an introduction and assuming no prior training in dynamic programming of any form, Approximate Dynamic Programming contains dozens of algorithms that are intended to serve as a starting point in the design of practical solutions for real problems. The book provides detailed coverage of implementation challenges including: modeling complex sequential decision processes under uncertainty, identifying robust policies, designing and estimating value function approximations, choosing effective stepsize rules, and resolving convergence issues. With a focus on modeling and algorithms in conjunction with the language of mainstream operations research, artificial intelligence, and control theory, Approximate Dynamic Programming: Models complex, high-dimensional problems in a natural and practical way, which draws on years of industrial projects Introduces and emphasizes the power of estimating a value function around the post-decision state, allowing solution algorithms to be broken down into three fundamental steps: classical simulation, classical optimization, and classical statistics Presents a thorough discussion of recursive estimation, including fundamental theory and a number of issues that arise in the development of practical algorithms Offers a variety of methods for approximating dynamic programs that have appeared in previous literature, but that have never been presented in the coherent format of a book Motivated by examples from modern-day operations research, Approximate Dynamic Programming is an accessible introduction to dynamic modeling and is also a valuable guide for the development of high-quality solutions to problems that exist in operations research and engineering. The clear and precise presentation of the material makes this an appropriate text for advanced undergraduate and beginning graduate courses, while also serving as a reference for researchers and practitioners. A companion Web site is available for readers, which includes additional exercises, solutions to exercises, and data sets to reinforce the book's main concepts.

Optimization of Temporal Networks under Uncertainty

Author : Wolfram Wiesemann
Publisher : Springer Science & Business Media
ISBN 13 : 3642234275
Total Pages : 168 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Optimization of Temporal Networks under Uncertainty by : Wolfram Wiesemann

Download or read book Optimization of Temporal Networks under Uncertainty written by Wolfram Wiesemann and published by Springer Science & Business Media. This book was released on 2012-01-04 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many decision problems in Operations Research are defined on temporal networks, that is, workflows of time-consuming tasks whose processing order is constrained by precedence relations. For example, temporal networks are used to model projects, computer applications, digital circuits and production processes. Optimization problems arise in temporal networks when a decision maker wishes to determine a temporal arrangement of the tasks and/or a resource assignment that optimizes some network characteristic (e.g. the time required to complete all tasks). The parameters of these optimization problems (e.g. the task durations) are typically unknown at the time the decision problem arises. This monograph investigates solution techniques for optimization problems in temporal networks that explicitly account for this parameter uncertainty. We study several formulations, each of which requires different information about the uncertain problem parameters.