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Author: SeChan Oh Publisher: ISBN: Category : Languages : en Pages :
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.
Author: SeChan Oh Publisher: ISBN: Category : Languages : en Pages :
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.
Author: SeChan Oh Publisher: Stanford University ISBN: Category : Languages : en Pages : 159
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.
Author: Goran Peskir Publisher: Springer Science & Business Media ISBN: 3764373903 Category : Mathematics Languages : en Pages : 515
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.
Author: Svetlana Boyarchenko Publisher: Springer Science & Business Media ISBN: 3540737464 Category : Business & Economics Languages : en Pages : 292
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.
Author: Bradley Sturt Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
Optimal stopping is a fundamental class of stochastic dynamic optimization problems with numerous applications in finance and operations management. We introduce a new approach for solving computationally-demanding stochastic optimal stopping problems with known probability distributions. The approach uses simulation to construct a robust optimization problem that approximates the stochastic optimal stopping problem to any arbitrary accuracy; we then solve the robust optimization problem to obtain near-optimal Markovian stopping rules for the stochastic optimal stopping problem.In this paper, we focus on designing algorithms for solving the robust optimization problems that approximate the stochastic optimal stopping problems. These robust optimization problems are challenging to solve because they require optimizing over the infinite-dimensional space of all Markovian stopping rules. We overcome this challenge by characterizing the structure of optimal Markovian stopping rules for the robust optimization problems. In particular, we show that optimal Markovian stopping rules for the robust optimization problems have a structure that is surprisingly simple and finite-dimensional. We leverage this structure to develop an exact reformulation of the robust optimization problem as a zero-one bilinear program over totally unimodular constraints. We show that the bilinear program can be solved in polynomial time in special cases, establish computational complexity results for general cases, and develop polynomial-time heuristics by relating the bilinear program to the maximal closure problem from graph theory. Numerical experiments demonstrate that our algorithms for solving the robust optimization problems are practical and can outperform state-of-the-art simulation-based algorithms in the context of widely-studied stochastic optimal stopping problems from high-dimensional option pricing.
Author: Anbazhagan, Neelamegam Publisher: IGI Global ISBN: 1522500456 Category : Business & Economics Languages : en Pages : 359
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.
Author: Denis Belomestny Publisher: Springer ISBN: 1137033517 Category : Business & Economics Languages : en Pages : 366
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.
Author: Christiane Barz Publisher: Springer Science & Business Media ISBN: 3540730141 Category : Business & Economics Languages : en Pages : 173
Book Description
This book revises the well-known capacity control problem in revenue management from the perspective of a risk-averse decision-maker. Modelling an expected utility maximizing decision maker, the problem is formulated as a risk-sensitive Markov decision process. Special emphasis is put on the existence of structured optimal policies. Numerical examples illustrate the results.
Author: SeChan Oh
Author: SeChan Oh
Author: SeChan Oh
Author: Goran Peskir
Author: Svetlana Boyarchenko
Author: Bradley Sturt
Author: Anbazhagan, Neelamegam
Author: Denis Belomestny
Author: Alfred Müller
Author: Christiane Barz
Author: Syouji Nakamura