Emanuel Todorov
- Published in print:
- 2006
- Published Online:
- August 2013
- ISBN:
- 9780262042383
- eISBN:
- 9780262294188
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262042383.003.0012
- Subject:
- Neuroscience, Disorders of the Nervous System
Optimal control theory is a mathematical discipline for studying the neural control of movement. This chapter presents a mathematical introduction to optimal control theory and discusses the ...
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Optimal control theory is a mathematical discipline for studying the neural control of movement. This chapter presents a mathematical introduction to optimal control theory and discusses the following topics: Bellman equations, Hamilton-Jacobi-Bellman equations, Ricatti equations, and Kalman filter. It also examines the duality of optimal control and optimal estimation, and, finally, describes optimal control models and suggests future research directions.Less
Optimal control theory is a mathematical discipline for studying the neural control of movement. This chapter presents a mathematical introduction to optimal control theory and discusses the following topics: Bellman equations, Hamilton-Jacobi-Bellman equations, Ricatti equations, and Kalman filter. It also examines the duality of optimal control and optimal estimation, and, finally, describes optimal control models and suggests future research directions.
Robert C. Merton
- Published in print:
- 2006
- Published Online:
- January 2009
- ISBN:
- 9780199298839
- eISBN:
- 9780191711480
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199298839.003.0019
- Subject:
- Economics and Finance, History of Economic Thought
This chapter's appraisal places models of time and uncertainty in household allocation of resources at the center of the Samuelson Contribution. It assesses Samuelson's contributions to the areas of ...
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This chapter's appraisal places models of time and uncertainty in household allocation of resources at the center of the Samuelson Contribution. It assesses Samuelson's contributions to the areas of efficient market theory and risk analysis, portfolio selection, and option and warrant pricing. Samuelson found that efficient markets do not allocate resources the way casinos do. Rather, asset prices vary randomly around an optimal path that can be discerned mathematically. The theory links spot price with future prices in order to forge a solution where spot prices are determined by optimal control theory. Samuelson's work in warrants and option pricing provides a bridge between early and later option pricing models, thanks to his insights on hedging and mathematical analysis that were incorporated into subsequent theories.Less
This chapter's appraisal places models of time and uncertainty in household allocation of resources at the center of the Samuelson Contribution. It assesses Samuelson's contributions to the areas of efficient market theory and risk analysis, portfolio selection, and option and warrant pricing. Samuelson found that efficient markets do not allocate resources the way casinos do. Rather, asset prices vary randomly around an optimal path that can be discerned mathematically. The theory links spot price with future prices in order to forge a solution where spot prices are determined by optimal control theory. Samuelson's work in warrants and option pricing provides a bridge between early and later option pricing models, thanks to his insights on hedging and mathematical analysis that were incorporated into subsequent theories.
Thomas A. Weber
- Published in print:
- 2011
- Published Online:
- August 2013
- ISBN:
- 9780262015738
- eISBN:
- 9780262298483
- Item type:
- book
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262015738.001.0001
- Subject:
- Mathematics, Probability / Statistics
This book bridges optimal control theory and economics, discussing ordinary differential equations (ODEs), optimal control, game theory, and mechanism design in one volume. Technically rigorous and ...
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This book bridges optimal control theory and economics, discussing ordinary differential equations (ODEs), optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations is the backbone of the theory developed in the book, and Chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendices provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer’s creation of an environment in which players interact to maximize the designer’s objective. The book focuses on applications; the problems are an integral part of the text.Less
This book bridges optimal control theory and economics, discussing ordinary differential equations (ODEs), optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations is the backbone of the theory developed in the book, and Chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendices provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer’s creation of an environment in which players interact to maximize the designer’s objective. The book focuses on applications; the problems are an integral part of the text.
Dipankar Dasgupta
- Published in print:
- 2010
- Published Online:
- October 2012
- ISBN:
- 9780198069966
- eISBN:
- 9780199080458
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198069966.001.0001
- Subject:
- Economics and Finance, Macro- and Monetary Economics
This book is about growth theory, an important subject taught as a part of economic theory. It introduces the literature on growth and inequality and examines Charles Jones’s views on growth ...
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This book is about growth theory, an important subject taught as a part of economic theory. It introduces the literature on growth and inequality and examines Charles Jones’s views on growth economics. This book examines key economic issues ranging from long-run growth to taxation policies for growth, growth and infrastructure, human capital formation, intuitive as well as rigorous development of optimal control theory using undergraduate mathematical tools, and a unified theoretical framework to help students shift their focus from old growth theory to modern growth theory. The book also presents an analysis of India’s long-term growth experience.Less
This book is about growth theory, an important subject taught as a part of economic theory. It introduces the literature on growth and inequality and examines Charles Jones’s views on growth economics. This book examines key economic issues ranging from long-run growth to taxation policies for growth, growth and infrastructure, human capital formation, intuitive as well as rigorous development of optimal control theory using undergraduate mathematical tools, and a unified theoretical framework to help students shift their focus from old growth theory to modern growth theory. The book also presents an analysis of India’s long-term growth experience.
Carsten A. Ullrich
- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199563029
- eISBN:
- 9780191775130
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199563029.003.0016
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter focuses on electronic phenomena that occur when atoms and molecules are exposed to strong and short laser pulses. Under these conditions, the external potential cannot be treated as a ...
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This chapter focuses on electronic phenomena that occur when atoms and molecules are exposed to strong and short laser pulses. Under these conditions, the external potential cannot be treated as a small perturbation. Several highly nonlinear effects are introduced and reviewed: multiphoton ionization, above-threshold ionization, and high-harmonic generation. The performance of time-dependent density-functional theory for these phenomena is discussed. A particular challenge is the enhancement of double ionization in rare-gas atoms, such as the so-called helium knee, due to strong correlation effects. This puts stringent demands on the exchange-correlation functional, and on the way in which one calculates ionization yields. Time-dependent density-functional theory has been successfully used to calculate high-harmonic spectra in atoms and molecules. Finally, the basics of optimal control theory are reviewed, and illustrated with an example. It is shown how control theory and time-dependent density-functional theory can be combined.Less
This chapter focuses on electronic phenomena that occur when atoms and molecules are exposed to strong and short laser pulses. Under these conditions, the external potential cannot be treated as a small perturbation. Several highly nonlinear effects are introduced and reviewed: multiphoton ionization, above-threshold ionization, and high-harmonic generation. The performance of time-dependent density-functional theory for these phenomena is discussed. A particular challenge is the enhancement of double ionization in rare-gas atoms, such as the so-called helium knee, due to strong correlation effects. This puts stringent demands on the exchange-correlation functional, and on the way in which one calculates ionization yields. Time-dependent density-functional theory has been successfully used to calculate high-harmonic spectra in atoms and molecules. Finally, the basics of optimal control theory are reviewed, and illustrated with an example. It is shown how control theory and time-dependent density-functional theory can be combined.
Thomas A. Weber
- Published in print:
- 2011
- Published Online:
- August 2013
- ISBN:
- 9780262015738
- eISBN:
- 9780262298483
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262015738.003.0005
- Subject:
- Mathematics, Probability / Statistics
This chapter reviews the basics of static mechanism design in settings where a principal faces a single agent of uncertain type. The aim of the resulting screening contract is for the principal to ...
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This chapter reviews the basics of static mechanism design in settings where a principal faces a single agent of uncertain type. The aim of the resulting screening contract is for the principal to obtain the agent’s type information in order to avert adverse selection, maximizing her payoffs. Nonlinear pricing is discussed as an application of optimal control theory.Less
This chapter reviews the basics of static mechanism design in settings where a principal faces a single agent of uncertain type. The aim of the resulting screening contract is for the principal to obtain the agent’s type information in order to avert adverse selection, maximizing her payoffs. Nonlinear pricing is discussed as an application of optimal control theory.
