Optimal Stopping Problems in Operations Management

Optimal Stopping Problems in Operations Management PDF Author: SeChan Oh
Publisher: Stanford University
ISBN:
Category :
Languages : en
Pages : 159

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Book Description
Optimal stopping problems determine the time to terminate a process to maximize expected rewards. Such problems are pervasive in the areas of operations management, marketing, statistics, finance, and economics. This dissertation provides a method that characterizes the structure of the optimal stopping policy for a general class of optimal stopping problems. It also studies two important optimal stopping problems arising in Operations Management. In the first part of the dissertation, we provide a method to characterize the structure of the optimal stopping policy for the class of discrete-time optimal stopping problems. Our method characterizes the structure of the optimal policy for some stopping problems for which conventional methods fail. Our method also simplifies the analysis of some existing results. Using the method, we determine sufficient conditions that yield threshold or control-band type optimal stopping policies. The results also help characterize parametric monotonicity of optimal thresholds and provide bounds for them. In the second part of the dissertation, we first generalize the Martingale Model of Forecast Evolution to account for multiple forecasters who forecast demand for the same product. The result enables us to consistently model the evolution of forecasts generated by two forecasters who have asymmetric demand information. Using the forecast evolution model, we next study a supplier's problem of eliciting credible forecast information from a manufacturer when both parties obtain asymmetric demand information over multiple periods. For better capacity planning, the supplier designs and offers a screening contract that ensures the manufacturer's credible information sharing. By delaying to offer this incentive mechanism, the supplier can obtain more information. This delay, however, may increase (resp., or decrease) the degree of information asymmetry between the two firms, resulting in a higher (resp., or lower) cost of screening. The delay may also increase capacity costs. Considering all such trade-offs, the supplier has to determine how to design a mechanism to elicit credible forecast information from the manufacturer and when to offer this incentive mechanism. In the last part of the dissertation, we study a manufacturer's problem of determining the time to introduce a new product to the market. Conventionally, manufacturing firms determine the time to introduce a new product to the market long before launching the product. The timing decision involves considerable risk because manufacturing firms are uncertain about competing firms' market entry timing and the outcome of production process development activities at the time when they make the decision. As a solution for reducing such risk, we propose a dynamic market entry strategy under which the manufacturer makes decisions about market entry timing and process improvements in response to the evolution of uncertain factors. We show that the manufacturer can reduce profit variability and increase average profit by employing this dynamic strategy. Our study also characterizes the industry conditions under which the dynamic strategy is most effective.

Optimal Stopping Problems in Operations Management

Optimal Stopping Problems in Operations Management PDF Author: SeChan Oh
Publisher: Stanford University
ISBN:
Category :
Languages : en
Pages : 159

Get Book Here

Book Description
Optimal stopping problems determine the time to terminate a process to maximize expected rewards. Such problems are pervasive in the areas of operations management, marketing, statistics, finance, and economics. This dissertation provides a method that characterizes the structure of the optimal stopping policy for a general class of optimal stopping problems. It also studies two important optimal stopping problems arising in Operations Management. In the first part of the dissertation, we provide a method to characterize the structure of the optimal stopping policy for the class of discrete-time optimal stopping problems. Our method characterizes the structure of the optimal policy for some stopping problems for which conventional methods fail. Our method also simplifies the analysis of some existing results. Using the method, we determine sufficient conditions that yield threshold or control-band type optimal stopping policies. The results also help characterize parametric monotonicity of optimal thresholds and provide bounds for them. In the second part of the dissertation, we first generalize the Martingale Model of Forecast Evolution to account for multiple forecasters who forecast demand for the same product. The result enables us to consistently model the evolution of forecasts generated by two forecasters who have asymmetric demand information. Using the forecast evolution model, we next study a supplier's problem of eliciting credible forecast information from a manufacturer when both parties obtain asymmetric demand information over multiple periods. For better capacity planning, the supplier designs and offers a screening contract that ensures the manufacturer's credible information sharing. By delaying to offer this incentive mechanism, the supplier can obtain more information. This delay, however, may increase (resp., or decrease) the degree of information asymmetry between the two firms, resulting in a higher (resp., or lower) cost of screening. The delay may also increase capacity costs. Considering all such trade-offs, the supplier has to determine how to design a mechanism to elicit credible forecast information from the manufacturer and when to offer this incentive mechanism. In the last part of the dissertation, we study a manufacturer's problem of determining the time to introduce a new product to the market. Conventionally, manufacturing firms determine the time to introduce a new product to the market long before launching the product. The timing decision involves considerable risk because manufacturing firms are uncertain about competing firms' market entry timing and the outcome of production process development activities at the time when they make the decision. As a solution for reducing such risk, we propose a dynamic market entry strategy under which the manufacturer makes decisions about market entry timing and process improvements in response to the evolution of uncertain factors. We show that the manufacturer can reduce profit variability and increase average profit by employing this dynamic strategy. Our study also characterizes the industry conditions under which the dynamic strategy is most effective.

Advanced Simulation-Based Methods for Optimal Stopping and Control

Advanced Simulation-Based Methods for Optimal Stopping and Control PDF Author: Denis Belomestny
Publisher: Springer
ISBN: 1137033517
Category : Business & Economics
Languages : en
Pages : 366

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Book Description
This is an advanced guide to optimal stopping and control, focusing on advanced Monte Carlo simulation and its application to finance. Written for quantitative finance practitioners and researchers in academia, the book looks at the classical simulation based algorithms before introducing some of the new, cutting edge approaches under development.

Algorithms to Live By

Algorithms to Live By PDF Author: Brian Christian
Publisher: Macmillan
ISBN: 1627790365
Category : Business & Economics
Languages : en
Pages : 366

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Book Description
'Algorithms to Live By' looks at the simple, precise algorithms that computers use to solve the complex 'human' problems that we face, and discovers what they can tell us about the nature and origin of the mind.

Irreversible Decisions under Uncertainty

Irreversible Decisions under Uncertainty PDF Author: Svetlana Boyarchenko
Publisher: Springer Science & Business Media
ISBN: 3540737464
Category : Business & Economics
Languages : en
Pages : 292

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Book Description
Here, two highly experienced authors present an alternative approach to optimal stopping problems. The basic ideas and techniques of the approach can be explained much simpler than the standard methods in the literature on optimal stopping problems. The monograph will teach the reader to apply the technique to many problems in economics and finance, including new ones. From the technical point of view, the method can be characterized as option pricing via the Wiener-Hopf factorization.

Multiple Stopping Problems

Multiple Stopping Problems PDF Author: Georgy Sofronov
Publisher: CRC Press
ISBN: 1040228925
Category : Mathematics
Languages : en
Pages : 376

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Book Description
This book presents the theory of rational decisions involving the selection of stopping times in observed discrete-time stochastic processes, both by single and multiple decision-makers. Readers will become acquainted with the models, strategies, and applications of these models. It begins with an examination of selected models framed as stochastic optimization challenges, emphasizing the critical role of optimal stopping times in sequential statistical procedures. The authors go on to explore models featuring multiple stopping and shares on leading applications, particularly focusing on change point detection, selection problems, and the nuances of behavioral ecology. In the following chapters, an array of perspectives on model strategies is presented, elucidating their interpretation and the methodologies underpinning their genesis. Essential notations and definitions are introduced, examining general theorems about solution existence and structure, with an intricate analysis of optimal stopping predicaments and addressing crucial multilateral models. The reader is presented with the practical application of models based on multiple stopping within stochastic processes. The coverage includes a diverse array of domains, including sequential statistics, finance, economics, and the broader generalization of the best-choice problem. Additionally, it delves into numerical and asymptotic solutions, offering a comprehensive exploration of optimal stopping quandaries. The book will be of interest to researchers and practitioners in fields such as economics, finance, and engineering. It could also be used by graduate students doing a research degree in insurance, economics or business analytics or an advanced undergraduate course in mathematical sciences.

Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE

Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE PDF Author: Nizar Touzi
Publisher: Springer Science & Business Media
ISBN: 1461442869
Category : Mathematics
Languages : en
Pages : 219

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Book Description
This book collects some recent developments in stochastic control theory with applications to financial mathematics. We first address standard stochastic control problems from the viewpoint of the recently developed weak dynamic programming principle. A special emphasis is put on the regularity issues and, in particular, on the behavior of the value function near the boundary. We then provide a quick review of the main tools from viscosity solutions which allow to overcome all regularity problems. We next address the class of stochastic target problems which extends in a nontrivial way the standard stochastic control problems. Here the theory of viscosity solutions plays a crucial role in the derivation of the dynamic programming equation as the infinitesimal counterpart of the corresponding geometric dynamic programming equation. The various developments of this theory have been stimulated by applications in finance and by relevant connections with geometric flows. Namely, the second order extension was motivated by illiquidity modeling, and the controlled loss version was introduced following the problem of quantile hedging. The third part specializes to an overview of Backward stochastic differential equations, and their extensions to the quadratic case.​

Optimal Stopping and Free-Boundary Problems

Optimal Stopping and Free-Boundary Problems PDF Author: Goran Peskir
Publisher: Springer Science & Business Media
ISBN: 3764373903
Category : Mathematics
Languages : en
Pages : 515

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Book Description
This book discloses a fascinating connection between optimal stopping problems in probability and free-boundary problems. It focuses on key examples and the theory of optimal stopping is exposed at its basic principles in discrete and continuous time covering martingale and Markovian methods. Methods of solution explained range from change of time, space, and measure, to more recent ones such as local time-space calculus and nonlinear integral equations. A chapter on stochastic processes makes the material more accessible. The book will appeal to those wishing to master stochastic calculus via fundamental examples. Areas of application include financial mathematics, financial engineering, and mathematical statistics.

An Annotated Timeline of Operations Research

An Annotated Timeline of Operations Research PDF Author: Saul I. Gass
Publisher: Springer Science & Business Media
ISBN: 1402081138
Category : Business & Economics
Languages : en
Pages : 221

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Book Description
An Annotated Timeline of Operations Research: An Informal History recounts the evolution of Operations Research (OR) as a new science - the science of decision making. Arising from the urgent operational issues of World War II, the philosophy and methodology of OR has permeated the resolution of decision problems in business, industry, and government. The Timeline chronicles the history of OR in the form of self-contained, expository entries. Each entry presents a concise explanation of the events and people under discussion, and provides key sources where further relevant information can be obtained. In addition, books and papers that have influenced the development of OR or helped to educate the first generations of OR academics and practitioners are cited throughout the book. Starting in 1564 with seminal ideas that form the precursors of OR, the Timeline traces the key ideas and events of OR through 2004. The Timeline should interest anyone involved in OR - researchers, practitioners, academics, and, especially, students - who wish to learn how OR came into being. Further, the scope and expository style of the Timeline should make it of value to the general reader interested in the development of science and technology in the last half of the twentieth century.

The Theory of Optimal Stopping

The Theory of Optimal Stopping PDF Author: Yuan Shih Chow
Publisher: Dover Publications
ISBN: 9780486666501
Category : Mathematics
Languages : en
Pages : 139

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Book Description


Stochastic Processes and Models in Operations Research

Stochastic Processes and Models in Operations Research PDF Author: Anbazhagan, Neelamegam
Publisher: IGI Global
ISBN: 1522500456
Category : Business & Economics
Languages : en
Pages : 359

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Book Description
Decision-making is an important task no matter the industry. Operations research, as a discipline, helps alleviate decision-making problems through the extraction of reliable information related to the task at hand in order to come to a viable solution. Integrating stochastic processes into operations research and management can further aid in the decision-making process for industrial and management problems. Stochastic Processes and Models in Operations Research emphasizes mathematical tools and equations relevant for solving complex problems within business and industrial settings. This research-based publication aims to assist scholars, researchers, operations managers, and graduate-level students by providing comprehensive exposure to the concepts, trends, and technologies relevant to stochastic process modeling to solve operations research problems.