Stochastic Control by Functional Analysis Methods
Author: A. Bensoussan
Publisher: Elsevier
Published: 2011-08-18
Total Pages: 427
ISBN-13: 0080875327
DOWNLOAD EBOOKStochastic Control by Functional Analysis Methods
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Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems
Author: Harold Kushner
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 245
ISBN-13: 146124482X
DOWNLOAD EBOOKThe book deals with several closely related topics concerning approxima tions and perturbations of random processes and their applications to some important and fascinating classes of problems in the analysis and design of stochastic control systems and nonlinear filters. The basic mathematical methods which are used and developed are those of the theory of weak con vergence. The techniques are quite powerful for getting weak convergence or functional limit theorems for broad classes of problems and many of the techniques are new. The original need for some of the techniques which are developed here arose in connection with our study of the particular applica tions in this book, and related problems of approximation in control theory, but it will be clear that they have numerous applications elsewhere in weak convergence and process approximation theory. The book is a continuation of the author's long term interest in problems of the approximation of stochastic processes and its applications to problems arising in control and communication theory and related areas. In fact, the techniques used here can be fruitfully applied to many other areas. The basic random processes of interest can be described by solutions to either (multiple time scale) Ito differential equations driven by wide band or state dependent wide band noise or which are singularly perturbed. They might be controlled or not, and their state values might be fully observable or not (e. g. , as in the nonlinear filtering problem).
Stochastic Optimal Control in Infinite Dimension
Author: Giorgio Fabbri
Publisher: Springer
Published: 2017-06-22
Total Pages: 928
ISBN-13: 3319530674
DOWNLOAD EBOOKProviding an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite dimension. Readers from other fields who want to learn the basic theory will also find it useful. The prerequisites are: standard functional analysis, the theory of semigroups of operators and its use in the study of PDEs, some knowledge of the dynamic programming approach to stochastic optimal control problems in finite dimension, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.
Stochastic Differential Systems, Stochastic Control Theory and Applications
Author: Wendell Fleming
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 601
ISBN-13: 1461387620
DOWNLOAD EBOOKThis IMA Volume in Mathematics and its Applications STOCHASTIC DIFFERENTIAL SYSTEMS, STOCHASTIC CONTROL THEORY AND APPLICATIONS is the proceedings of a workshop which was an integral part of the 1986-87 IMA program on STOCHASTIC DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS. We are grateful to the Scientific Committee: Daniel Stroock (Chairman) WendeIl Flerning Theodore Harris Pierre-Louis Lions Steven Orey George Papanicolaou for planning and implementing an exciting and stimulating year-long program. We es pecially thank WendeIl Fleming and Pierre-Louis Lions for organizing an interesting and productive workshop in an area in which mathematics is beginning to make significant contributions to real-world problems. George R. Seil Hans Weinberger PREFACE This volume is the Proceedings of a Workshop on Stochastic Differential Systems, Stochastic Control Theory, and Applications held at IMA June 9-19,1986. The Workshop Program Commit tee consisted of W.H. Fleming and P.-L. Lions (co-chairmen), J. Baras, B. Hajek, J.M. Harrison, and H. Sussmann. The Workshop emphasized topics in the following four areas. (1) Mathematical theory of stochastic differential systems, stochastic control and nonlinear filtering for Markov diffusion processes. Connections with partial differential equations. (2) Applications of stochastic differential system theory, in engineering and management sci ence. Adaptive control of Markov processes. Advanced computational methods in stochas tic control and nonlinear filtering. (3) Stochastic scheduling, queueing networks, and related topics. Flow control, multiarm bandit problems, applications to problems of computer networks and scheduling of complex manufacturing operations.
Numerical Methods for Stochastic Control Problems in Continuous Time
Author: Harold Kushner
Publisher: Springer Science & Business Media
Published: 2013-11-27
Total Pages: 480
ISBN-13: 146130007X
DOWNLOAD EBOOKStochastic control is a very active area of research. This monograph, written by two leading authorities in the field, has been updated to reflect the latest developments. It covers effective numerical methods for stochastic control problems in continuous time on two levels, that of practice and that of mathematical development. It is broadly accessible for graduate students and researchers.
Continuous-time Stochastic Control and Optimization with Financial Applications
Author: Huyên Pham
Publisher: Springer Science & Business Media
Published: 2009-05-28
Total Pages: 243
ISBN-13: 3540895000
DOWNLOAD EBOOKStochastic 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.
Proceedings of the International Congress of Mathematicians 2010 (icm 2010) (in 4 Volumes) - Vol. I: Plenary Lectures and Ceremonies, Vols. Ii-iv: Invited Lectures
Author:
Publisher: World Scientific
Published: 2011
Total Pages: 814
ISBN-13: 9814324353
DOWNLOAD EBOOKProceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures
Author: Rajendra Bhatia
Publisher: World Scientific
Published: 2011-06-06
Total Pages: 4137
ISBN-13: 9814462934
DOWNLOAD EBOOKICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
Optimal Pricing, Inflation, and the Cost of Price Adjustment
Author: Eytan Sheshinski
Publisher: MIT Press
Published: 1993
Total Pages: 546
ISBN-13: 9780262193320
DOWNLOAD EBOOKThese collected articles constitute what is perhaps the definitive study of pricing models under inflation, providing a solid basis for further research on this elusive question. What are the real effects of inflation? These collected articles constitute what is perhaps the definitive study of pricing models under inflation, providing a solid basis for further research on this elusive question. Covering a broad range of theory and applications by well-known microeconomists, the eighteen contributions evaluate the effects of inflation on aggregate output and on welfare and reveal the scope of recent efforts to explicitly incorporate frictions in economic models. A basic building block common to most of the essays in this volume is the observation that individual firms change nominal prices intermittently. The frequency and size of nominal price changes are influenced by the cost of price adjustment and changes in the economic environment, production costs, market demand, market structure, and most important, inflation. Thus the degree of nominal rigidity is influenced by the economic environment, and in a dynamic context. Two introductory essays survey the empirical studies of pricing policies by individual firms and the theoretical efforts to integrate the nominal rigidities at the micro level into macro relationships. The essays that follow treat the general problem of optimal dynamic adjustment in the presence of convex costs of adjustment, include applications of the inventory models to the case of nominal price adjustment by an individual firm, address the question of aggregation, introduce active search by consumers, and provide empirical analysis of nominal price rigidities.
Engineering Risk and Finance
Author: Charles S. Tapiero
Publisher: Springer Science & Business Media
Published: 2013-02-13
Total Pages: 518
ISBN-13: 1461462347
DOWNLOAD EBOOKRisk models are models of uncertainty, engineered for some purposes. They are “educated guesses and hypotheses” assessed and valued in terms of well-defined future states and their consequences. They are engineered to predict, to manage countable and accountable futures and to provide a frame of reference within which we may believe that “uncertainty is tamed”. Quantitative-statistical tools are used to reconcile our information, experience and other knowledge with hypotheses that both serve as the foundation of risk models and also value and price risk. Risk models are therefore common to most professions, each with its own methods and techniques based on their needs, experience and a wisdom accrued over long periods of time. This book provides a broad and interdisciplinary foundation to engineering risks and to their financial valuation and pricing. Risk models applied in industry and business, heath care, safety, the environment and regulation are used to highlight their variety while financial valuation techniques are used to assess their financial consequences. This book is technically accessible to all readers and students with a basic background in probability and statistics (with 3 chapters devoted to introduce their elements). Principles of risk measurement, valuation and financial pricing as well as the economics of uncertainty are outlined in 5 chapters with numerous examples and applications. New results, extending classical models such as the CCAPM are presented providing insights to assess the risks and their price in an interconnected, dependent and strategic economic environment. In an environment departing from the fundamental assumptions we make regarding financial markets, the book provides a strategic/game-like approach to assess the risk and the opportunities that such an environment implies. To control these risks, a strategic-control approach is developed that recognizes that many risks resulting by “what we do” as well as “what others do”. In particular we address the strategic and statistical control of compliance in large financial institutions confronted increasingly with a complex and far more extensive regulation.
