Mathematical Control Theory And Finance

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Mathematical Control Theory and Finance

Author : Andrey Sarychev
Publisher : Springer Science & Business Media
ISBN 13 : 354069532X
Total Pages : 418 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Mathematical Control Theory and Finance by : Andrey Sarychev

Download or read book Mathematical Control Theory and Finance written by Andrey Sarychev and published by Springer Science & Business Media. This book was released on 2009-03-31 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control theory provides a large set of theoretical and computational tools with applications in a wide range of ?elds, running from ”pure” branches of mathematics, like geometry, to more applied areas where the objective is to ?nd solutions to ”real life” problems, as is the case in robotics, control of industrial processes or ?nance. The ”high tech” character of modern business has increased the need for advanced methods. These rely heavily on mathematical techniques and seem indispensable for competitiveness of modern enterprises. It became essential for the ?nancial analyst to possess a high level of mathematical skills. C- versely, the complex challenges posed by the problems and models relevant to ?nance have, for a long time, been an important source of new research topics for mathematicians. The use of techniques from stochastic optimal control constitutes a well established and important branch of mathematical ?nance. Up to now, other branches of control theory have found comparatively less application in ?n- cial problems. To some extent, deterministic and stochastic control theories developed as di?erent branches of mathematics. However, there are many points of contact between them and in recent years the exchange of ideas between these ?elds has intensi?ed. Some concepts from stochastic calculus (e.g., rough paths) havedrawntheattentionofthedeterministiccontroltheorycommunity.Also, some ideas and tools usual in deterministic control (e.g., geometric, algebraic or functional-analytic methods) can be successfully applied to stochastic c- trol.

Mathematical Control Theory

Author : Jerzy Zabczyk
Publisher : Springer Science & Business Media
ISBN 13 : 9780817647322
Total Pages : 276 pages
Book Rating : 4.6/5 (473 download)

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Book Synopsis Mathematical Control Theory by : Jerzy Zabczyk

Download or read book Mathematical Control Theory written by Jerzy Zabczyk and published by Springer Science & Business Media. This book was released on 2008 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a mathematically precise manner, this book presents a unified introduction to deterministic control theory. It includes material on the realization of both linear and nonlinear systems, impulsive control, and positive linear systems.

Time-Inconsistent Control Theory with Finance Applications

Author : Tomas Björk
Publisher : Springer Nature
ISBN 13 : 3030818438
Total Pages : 328 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Time-Inconsistent Control Theory with Finance Applications by : Tomas Björk

Download or read book Time-Inconsistent Control Theory with Finance Applications written by Tomas Björk and published by Springer Nature. This book was released on 2021-11-02 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to problems of stochastic control and stopping that are time inconsistent in the sense that they do not admit a Bellman optimality principle. These problems are cast in a game-theoretic framework, with the focus on subgame-perfect Nash equilibrium strategies. The general theory is illustrated with a number of finance applications. In dynamic choice problems, time inconsistency is the rule rather than the exception. Indeed, as Robert H. Strotz pointed out in his seminal 1955 paper, relaxing the widely used ad hoc assumption of exponential discounting gives rise to time inconsistency. Other famous examples of time inconsistency include mean-variance portfolio choice and prospect theory in a dynamic context. For such models, the very concept of optimality becomes problematic, as the decision maker’s preferences change over time in a temporally inconsistent way. In this book, a time-inconsistent problem is viewed as a non-cooperative game between the agent’s current and future selves, with the objective of finding intrapersonal equilibria in the game-theoretic sense. A range of finance applications are provided, including problems with non-exponential discounting, mean-variance objective, time-inconsistent linear quadratic regulator, probability distortion, and market equilibrium with time-inconsistent preferences. Time-Inconsistent Control Theory with Finance Applications offers the first comprehensive treatment of time-inconsistent control and stopping problems, in both continuous and discrete time, and in the context of finance applications. Intended for researchers and graduate students in the fields of finance and economics, it includes a review of the standard time-consistent results, bibliographical notes, as well as detailed examples showcasing time inconsistency problems. For the reader unacquainted with standard arbitrage theory, an appendix provides a toolbox of material needed for the book.

Introduction to the Mathematical Theory of Control

Author : Alberto Bressan
Publisher :
ISBN 13 :
Total Pages : 336 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Introduction to the Mathematical Theory of Control by : Alberto Bressan

Download or read book Introduction to the Mathematical Theory of Control written by Alberto Bressan and published by . This book was released on 2007 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Primer on the Calculus of Variations and Optimal Control Theory

Author : Mike Mesterton-Gibbons
Publisher : American Mathematical Soc.
ISBN 13 : 0821847724
Total Pages : 274 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Primer on the Calculus of Variations and Optimal Control Theory by : Mike Mesterton-Gibbons

Download or read book A Primer on the Calculus of Variations and Optimal Control Theory written by Mike Mesterton-Gibbons and published by American Mathematical Soc.. This book was released on 2009 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The calculus of variations is used to find functions that optimize quantities expressed in terms of integrals. Optimal control theory seeks to find functions that minimize cost integrals for systems described by differential equations. This book is an introduction to both the classical theory of the calculus of variations and the more modern developments of optimal control theory from the perspective of an applied mathematician. It focuses on understanding concepts and how to apply them. The range of potential applications is broad: the calculus of variations and optimal control theory have been widely used in numerous ways in biology, criminology, economics, engineering, finance, management science, and physics. Applications described in this book include cancer chemotherapy, navigational control, and renewable resource harvesting. The prerequisites for the book are modest: the standard calculus sequence, a first course on ordinary differential equations, and some facility with the use of mathematical software. It is suitable for an undergraduate or beginning graduate course, or for self study. It provides excellent preparation for more advanced books and courses on the calculus of variations and optimal control theory.

An Introduction to Optimal Control Problems in Life Sciences and Economics

Author : Sebastian Aniţa
Publisher : Springer Science & Business Media
ISBN 13 : 0817680985
Total Pages : 232 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis An Introduction to Optimal Control Problems in Life Sciences and Economics by : Sebastian Aniţa

Download or read book An Introduction to Optimal Control Problems in Life Sciences and Economics written by Sebastian Aniţa and published by Springer Science & Business Media. This book was released on 2011-05-05 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining control theory and modeling, this textbook introduces and builds on methods for simulating and tackling concrete problems in a variety of applied sciences. Emphasizing "learning by doing," the authors focus on examples and applications to real-world problems. An elementary presentation of advanced concepts, proofs to introduce new ideas, and carefully presented MATLAB® programs help foster an understanding of the basics, but also lead the way to new, independent research. With minimal prerequisites and exercises in each chapter, this work serves as an excellent textbook and reference for graduate and advanced undergraduate students, researchers, and practitioners in mathematics, physics, engineering, computer science, as well as biology, biotechnology, economics, and finance.

Methods of Mathematical Finance

Author : Ioannis Karatzas
Publisher : Springer
ISBN 13 : 1493968459
Total Pages : 415 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Methods of Mathematical Finance by : Ioannis Karatzas

Download or read book Methods of Mathematical Finance written by Ioannis Karatzas and published by Springer. This book was released on 2017-01-10 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This sequel to Brownian Motion and Stochastic Calculus by the same authors develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets, within the context of Brownian-motion-driven asset prices. The latter topic is extended to a study of equilibrium, providing conditions for existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the book. This book will be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options.

Mathematical Control Theory

Author : Jerzy Zabczyk
Publisher : Springer Nature
ISBN 13 : 3030447782
Total Pages : 347 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Mathematical Control Theory by : Jerzy Zabczyk

Download or read book Mathematical Control Theory written by Jerzy Zabczyk and published by Springer Nature. This book was released on 2020-06-20 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents, in a mathematically precise manner, a unified introduction to deterministic control theory. With the exception of a few more advanced concepts required for the final part of the book, the presentation requires only a knowledge of basic facts from linear algebra, differential equations, and calculus. In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimensional systems, and the solution of minimum energy problems. This second edition includes new chapters that introduce a variety of topics, such as controllability with vanishing energy, boundary control systems, and delayed systems. With additional proofs, theorems, results, and a substantially larger index, this new edition will be an invaluable resource for students and researchers of control theory. Mathematical Control Theory: An Introduction will be ideal for a beginning graduate course in mathematical control theory, or for self-study by professionals needing a complete picture of the mathematical theory that underlies the applications of control theory. From reviews of the first edition: At last! We did need an introductory textbook on control which can be read, understood, and enjoyed by anyone. Gian-Carlo Rota, The Bulletin of Mathematics Books It covers a remarkable number of topics...The exposition is excellent, and the book is a joy to read. A novel one-semester course covering both linear and nonlinear systems could be given...The book is an excellent one for introducing a mathematician to control theory. Bulletin of the AMS Indeed, for mathematicians who look for the basic ideas or a general picture about the main branches of control theory, I believe this book can provide an excellent bridge to this area. IEEE Control Systems Magazine

Introduction to Mathematical Control Theory

Author : Stephen Barnett
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 424 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Introduction to Mathematical Control Theory by : Stephen Barnett

Download or read book Introduction to Mathematical Control Theory written by Stephen Barnett and published by Oxford University Press, USA. This book was released on 1985 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this new edition of a successful text, Professor Barnett, now joined in the authorship by Dr. Cameron, has concentrated on adding material where topics have developed since the first edition, and they have also taken advantage of the extensive classroom testing that has been possible in the intervening years. The book remains the concise readable account of some basic mathematical aspects of control, concentrating on state-space methods and emphasizing points of mathematical interest. As far as the additional material is concerned, the new chapter on multivariable theory reflects some of the significant developments in that field during the past decade, and there is also now an appendix on Kalman filtering. All references have been updated and a large number of new problems for student use have been incorporated.

Optimal Control Theory with Applications in Economics

Author : Thomas A. Weber
Publisher : MIT Press
ISBN 13 : 0262015730
Total Pages : 387 pages
Book Rating : 4.2/5 (62 download)

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Book Synopsis Optimal Control Theory with Applications in Economics by : Thomas A. Weber

Download or read book Optimal Control Theory with Applications in Economics written by Thomas A. Weber and published by MIT Press. This book was released on 2011-09-30 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to optimal control theory, with an emphasis on applications in economics. This book bridges optimal control theory and economics, discussing ordinary differential equations, 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 (ODEs) 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. Appendixes 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. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuous-time models.

Optimal Control Theory

Author : Suresh P. Sethi
Publisher : Springer Nature
ISBN 13 : 3030917452
Total Pages : 520 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Optimal Control Theory by : Suresh P. Sethi

Download or read book Optimal Control Theory written by Suresh P. Sethi and published by Springer Nature. This book was released on 2022-01-03 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new 4th edition offers an introduction to optimal control theory and its diverse applications in management science and economics. It introduces students to the concept of the maximum principle in continuous (as well as discrete) time by combining dynamic programming and Kuhn-Tucker theory. While some mathematical background is needed, the emphasis of the book is not on mathematical rigor, but on modeling realistic situations encountered in business and economics. It applies optimal control theory to the functional areas of management including finance, production and marketing, as well as the economics of growth and of natural resources. In addition, it features material on stochastic Nash and Stackelberg differential games and an adverse selection model in the principal-agent framework. Exercises are included in each chapter, while the answers to selected exercises help deepen readers’ understanding of the material covered. Also included are appendices of supplementary material on the solution of differential equations, the calculus of variations and its ties to the maximum principle, and special topics including the Kalman filter, certainty equivalence, singular control, a global saddle point theorem, Sethi-Skiba points, and distributed parameter systems. Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as the foundation for the book, in which the author applies it to business management problems developed from his own research and classroom instruction. The new edition has been refined and updated, making it a valuable resource for graduate courses on applied optimal control theory, but also for financial and industrial engineers, economists, and operational researchers interested in applying dynamic optimization in their fields.

Mathematical Finance

Author : Ernst Eberlein
Publisher : Springer Nature
ISBN 13 : 3030261069
Total Pages : 774 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Mathematical Finance by : Ernst Eberlein

Download or read book Mathematical Finance written by Ernst Eberlein and published by Springer Nature. This book was released on 2019-12-03 with total page 774 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taking continuous-time stochastic processes allowing for jumps as its starting and focal point, this book provides an accessible introduction to the stochastic calculus and control of semimartingales and explains the basic concepts of Mathematical Finance such as arbitrage theory, hedging, valuation principles, portfolio choice, and term structure modelling. It bridges thegap between introductory texts and the advanced literature in the field. Most textbooks on the subject are limited to diffusion-type models which cannot easily account for sudden price movements. Such abrupt changes, however, can often be observed in real markets. At the same time, purely discontinuous processes lead to a much wider variety of flexible and tractable models. This explains why processes with jumps have become an established tool in the statistics and mathematics of finance. Graduate students, researchers as well as practitioners will benefit from this monograph.

Mathematical Systems Theory in Biology, Communications, Computation and Finance

Author : Joachim Rosenthal
Publisher : Springer Science & Business Media
ISBN 13 : 0387216960
Total Pages : 508 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Mathematical Systems Theory in Biology, Communications, Computation and Finance by : Joachim Rosenthal

Download or read book Mathematical Systems Theory in Biology, Communications, Computation and Finance written by Joachim Rosenthal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains survey and research articles by some of the leading researchers in mathematical systems theory - a vibrant research area in its own right. Many authors have taken special care that their articles are self-contained and accessible also to non-specialists.

Optimal Control of Partial Differential Equations

Author : Fredi Tröltzsch
Publisher : American Mathematical Society
ISBN 13 : 1470476444
Total Pages : 417 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Optimal Control of Partial Differential Equations by : Fredi Tröltzsch

Download or read book Optimal Control of Partial Differential Equations written by Fredi Tröltzsch and published by American Mathematical Society. This book was released on 2024-03-21 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, second-order sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the Karush-Kuhn-Tucker theory of nonlinear programming in Banach spaces. The exposition begins with control problems with linear equations, quadratic cost functions and control constraints. To make the book self-contained, basic facts on weak solutions of elliptic and parabolic equations are introduced. Principles of functional analysis are introduced and explained as they are needed. Many simple examples illustrate the theory and its hidden difficulties. This start to the book makes it fairly self-contained and suitable for advanced undergraduates or beginning graduate students. Advanced control problems for nonlinear partial differential equations are also discussed. As prerequisites, results on boundedness and continuity of solutions to semilinear elliptic and parabolic equations are addressed. These topics are not yet readily available in books on PDEs, making the exposition also interesting for researchers. Alongside the main theme of the analysis of problems of optimal control, Tröltzsch also discusses numerical techniques. The exposition is confined to brief introductions into the basic ideas in order to give the reader an impression of how the theory can be realized numerically. After reading this book, the reader will be familiar with the main principles of the numerical analysis of PDE-constrained optimization.

Applications of Mathematical Control Theory to Finance. I. Modelling Simple Dynamic Cash Balance Problems

Author : Suresh P. Sethi
Publisher :
ISBN 13 :
Total Pages : 22 pages
Book Rating : 4.:/5 (233 download)

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Book Synopsis Applications of Mathematical Control Theory to Finance. I. Modelling Simple Dynamic Cash Balance Problems by : Suresh P. Sethi

Download or read book Applications of Mathematical Control Theory to Finance. I. Modelling Simple Dynamic Cash Balance Problems written by Suresh P. Sethi and published by . This book was released on 1970 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several simple models, discrete and continuous, are proposed for the problem of cash balances. This is the problem of a firm which must meet its demand for cash at minimum discounted cost during a horizon period. It is assumed that surplus cash is invested in securities. The model is solved by application mathematical control theory and the optimal policy is shown to depend upon the ratio of products of the future discount factors for cash and securities. (Author).

Advanced Mathematical Methods for Finance

Author : Julia Di Nunno
Publisher : Springer Science & Business Media
ISBN 13 : 364218412X
Total Pages : 532 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Advanced Mathematical Methods for Finance by : Julia Di Nunno

Download or read book Advanced Mathematical Methods for Finance written by Julia Di Nunno and published by Springer Science & Business Media. This book was released on 2011-03-29 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents innovations in the mathematical foundations of financial analysis and numerical methods for finance and applications to the modeling of risk. The topics selected include measures of risk, credit contagion, insider trading, information in finance, stochastic control and its applications to portfolio choices and liquidation, models of liquidity, pricing, and hedging. The models presented are based on the use of Brownian motion, Lévy processes and jump diffusions. Moreover, fractional Brownian motion and ambit processes are also introduced at various levels. The chosen blend of topics gives an overview of the frontiers of mathematics for finance. New results, new methods and new models are all introduced in different forms according to the subject. Additionally, the existing literature on the topic is reviewed. The diversity of the topics makes the book suitable for graduate students, researchers and practitioners in the areas of financial modeling and quantitative finance. The chapters will also be of interest to experts in the financial market interested in new methods and products. This volume presents the results of the European ESF research networking program Advanced Mathematical Methods for Finance.

Mathematical Methods in Robust Control of Discrete-Time Linear Stochastic Systems

Author : Vasile Dragan
Publisher : Springer Science & Business Media
ISBN 13 : 1441906304
Total Pages : 349 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Mathematical Methods in Robust Control of Discrete-Time Linear Stochastic Systems by : Vasile Dragan

Download or read book Mathematical Methods in Robust Control of Discrete-Time Linear Stochastic Systems written by Vasile Dragan and published by Springer Science & Business Media. This book was released on 2009-11-10 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph the authors develop a theory for the robust control of discrete-time stochastic systems, subjected to both independent random perturbations and to Markov chains. Such systems are widely used to provide mathematical models for real processes in fields such as aerospace engineering, communications, manufacturing, finance and economy. The theory is a continuation of the authors’ work presented in their previous book entitled "Mathematical Methods in Robust Control of Linear Stochastic Systems" published by Springer in 2006. Key features: - Provides a common unifying framework for discrete-time stochastic systems corrupted with both independent random perturbations and with Markovian jumps which are usually treated separately in the control literature; - Covers preliminary material on probability theory, independent random variables, conditional expectation and Markov chains; - Proposes new numerical algorithms to solve coupled matrix algebraic Riccati equations; - Leads the reader in a natural way to the original results through a systematic presentation; - Presents new theoretical results with detailed numerical examples. The monograph is geared to researchers and graduate students in advanced control engineering, applied mathematics, mathematical systems theory and finance. It is also accessible to undergraduate students with a fundamental knowledge in the theory of stochastic systems.