Methods Of Optimal Statistical Decisions Optimal Control And Stochastic Differential Equations

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Methods of Optimal Statistical Decisions, Optimal Control, and Stochastic Differential Equations

Ellida M. Khazen
Methods of Optimal Statistical Decisions Optimal Control and Stochastic Differential Equations Book PDF

Author : Ellida M. Khazen
Publisher : Xlibris Corporation
Page : 320 pages
File Size : 52,6 Mb
Release : 2009-11-16
Category : Education
ISBN : 9781462807178

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Methods of Optimal Statistical Decisions, Optimal Control, and Stochastic Differential Equations by Ellida M. Khazen Pdf

This book provides the reader with some insight into the mathematical models of random processes with continuous time, stochastic differential equations and stochastic integrals. An advanced development of the mathematical methods of optimal statistical decisions, statistical sequential analysis, and informational estimation of risks, and new methods and solutions to the important problems of the theory of optimal control are presented. The new original results obtained by this author and published shortly in her numerous scientific-research papers are presented in a systematic way in this book. The book is intended for engineers, students, post-graduate students, and scientist researchers. The presentation of the material is accessible to engineers.

Stochastic Optimal Control in Infinite Dimension

Giorgio Fabbri,Fausto Gozzi,Andrzej Święch
Stochastic Optimal Control in Infinite Dimension Book PDF

Author : Giorgio Fabbri,Fausto Gozzi,Andrzej Święch
Publisher : Springer
Page : 916 pages
File Size : 52,5 Mb
Release : 2017-06-22
Category : Mathematics
ISBN : 9783319530673

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Stochastic Optimal Control in Infinite Dimension by Giorgio Fabbri,Fausto Gozzi,Andrzej Święch Pdf

Providing 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.

Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE

Nizar Touzi
Optimal Stochastic Control Stochastic Target Problems and Backward SDE Book PDF

Author : Nizar Touzi
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 55,5 Mb
Release : 2012-09-25
Category : Mathematics
ISBN : 9781461442868

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Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE by Nizar Touzi Pdf

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.​

Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems

Jingrui Sun,Jiongmin Yong
Stochastic Linear Quadratic Optimal Control Theory Differential Games and Mean Field Problems Book PDF

Author : Jingrui Sun,Jiongmin Yong
Publisher : Springer Nature
Page : 138 pages
File Size : 50,5 Mb
Release : 2020-06-29
Category : Mathematics
ISBN : 9783030483067

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Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems by Jingrui Sun,Jiongmin Yong Pdf

This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents results for two-player differential games and mean-field optimal control problems in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, the book identifies, for the first time, the interconnections between the existence of open-loop and closed-loop Nash equilibria, solvability of the optimality system, and solvability of the associated Riccati equation, and also explores the open-loop solvability of mean-filed linear-quadratic optimal control problems. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.

Continuous-time Stochastic Control and Optimization with Financial Applications

Huyên Pham
Continuous time Stochastic Control and Optimization with Financial Applications Book PDF

Author : Huyên Pham
Publisher : Springer Science & Business Media
Page : 243 pages
File Size : 54,5 Mb
Release : 2009-05-28
Category : Mathematics
ISBN : 9783540895008

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Continuous-time Stochastic Control and Optimization with Financial Applications by Huyên Pham Pdf

Stochastic 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.

Deterministic and Stochastic Optimal Control

Wendell H. Fleming,Raymond W. Rishel
Deterministic and Stochastic Optimal Control Book PDF

Author : Wendell H. Fleming,Raymond W. Rishel
Publisher : Springer
Page : 222 pages
File Size : 40,7 Mb
Release : 2012-02-03
Category : Mathematics
ISBN : 1461263824

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Deterministic and Stochastic Optimal Control by Wendell H. Fleming,Raymond W. Rishel Pdf

This book may be regarded as consisting of two parts. In Chapters I-IV we pre sent what we regard as essential topics in an introduction to deterministic optimal control theory. This material has been used by the authors for one semester graduate-level courses at Brown University and the University of Kentucky. The simplest problem in calculus of variations is taken as the point of departure, in Chapter I. Chapters II, III, and IV deal with necessary conditions for an opti mum, existence and regularity theorems for optimal controls, and the method of dynamic programming. The beginning reader may find it useful first to learn the main results, corollaries, and examples. These tend to be found in the earlier parts of each chapter. We have deliberately postponed some difficult technical proofs to later parts of these chapters. In the second part of the book we give an introduction to stochastic optimal control for Markov diffusion processes. Our treatment follows the dynamic pro gramming method, and depends on the intimate relationship between second order partial differential equations of parabolic type and stochastic differential equations. This relationship is reviewed in Chapter V, which may be read inde pendently of Chapters I-IV. Chapter VI is based to a considerable extent on the authors' work in stochastic control since 1961. It also includes two other topics important for applications, namely, the solution to the stochastic linear regulator and the separation principle.

Random Evolutions and their Applications

Anatoly Swishchuk
Random Evolutions and their Applications Book PDF

Author : Anatoly Swishchuk
Publisher : Springer Science & Business Media
Page : 310 pages
File Size : 41,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401595988

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Random Evolutions and their Applications by Anatoly Swishchuk Pdf

The book is devoted to the new trends in random evolutions and their various applications to stochastic evolutionary sytems (SES). Such new developments as the analogue of Dynkin's formulae, boundary value problems, stochastic stability and optimal control of random evolutions, stochastic evolutionary equations driven by martingale measures are considered. The book also contains such new trends in applied probability as stochastic models of financial and insurance mathematics in an incomplete market. In the famous classical financial mathematics Black-Scholes model of a (B,S) market for securities prices, which is used for the description of the evolution of bonds and stocks prices and also for their derivatives, such as options, futures, forward contracts, etc., it is supposed that the dynamic of bonds and stocks prices are set by a linear differential and linear stochastic differential equations, respectively, with interest rate, appreciation rate and volatility such that they are predictable processes. Also, in the Arrow-Debreu economy, the securities prices which support a Radner dynamic equilibrium are a combination of an Ito process and a random point process, with the all coefficients and jumps being predictable processes.

Stochastic and Differential Games

Martino Bardi,T.E.S. Raghavan,T. Parthasarathy
Stochastic and Differential Games Book PDF

Author : Martino Bardi,T.E.S. Raghavan,T. Parthasarathy
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 52,8 Mb
Release : 1999-06
Category : Mathematics
ISBN : 0817640290

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Stochastic and Differential Games by Martino Bardi,T.E.S. Raghavan,T. Parthasarathy Pdf

The theory of two-person, zero-sum differential games started at the be­ ginning of the 1960s with the works of R. Isaacs in the United States and L. S. Pontryagin and his school in the former Soviet Union. Isaacs based his work on the Dynamic Programming method. He analyzed many special cases of the partial differential equation now called Hamilton­ Jacobi-Isaacs-briefiy HJI-trying to solve them explicitly and synthe­ sizing optimal feedbacks from the solution. He began a study of singular surfaces that was continued mainly by J. Breakwell and P. Bernhard and led to the explicit solution of some low-dimensional but highly nontriv­ ial games; a recent survey of this theory can be found in the book by J. Lewin entitled Differential Games (Springer, 1994). Since the early stages of the theory, several authors worked on making the notion of value of a differential game precise and providing a rigorous derivation of the HJI equation, which does not have a classical solution in most cases; we mention here the works of W. Fleming, A. Friedman (see his book, Differential Games, Wiley, 1971), P. P. Varaiya, E. Roxin, R. J. Elliott and N. J. Kalton, N. N. Krasovskii, and A. I. Subbotin (see their book Po­ sitional Differential Games, Nauka, 1974, and Springer, 1988), and L. D. Berkovitz. A major breakthrough was the introduction in the 1980s of two new notions of generalized solution for Hamilton-Jacobi equations, namely, viscosity solutions, by M. G. Crandall and P. -L.

Statistical and Mathematical Methods in Population Dynamics

R. Cavalloro
Statistical and Mathematical Methods in Population Dynamics Book PDF

Author : R. Cavalloro
Publisher : CRC Press
Page : 260 pages
File Size : 52,9 Mb
Release : 1984-06-01
Category : Medical
ISBN : 9061915481

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Statistical and Mathematical Methods in Population Dynamics by R. Cavalloro Pdf

Modelling and estimation of pest population, Data collection and analysis in pest control, Methods for pest control, Pest management systems.

Forward-Backward Stochastic Differential Equations and their Applications

Jin Ma,Jiongmin Yong
Forward Backward Stochastic Differential Equations and their Applications Book PDF

Author : Jin Ma,Jiongmin Yong
Publisher : Springer
Page : 278 pages
File Size : 46,8 Mb
Release : 2007-04-24
Category : Mathematics
ISBN : 9783540488316

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Forward-Backward Stochastic Differential Equations and their Applications by Jin Ma,Jiongmin Yong Pdf

This volume is a survey/monograph on the recently developed theory of forward-backward stochastic differential equations (FBSDEs). Basic techniques such as the method of optimal control, the 'Four Step Scheme', and the method of continuation are presented in full. Related topics such as backward stochastic PDEs and many applications of FBSDEs are also discussed in detail. The volume is suitable for readers with basic knowledge of stochastic differential equations, and some exposure to the stochastic control theory and PDEs. It can be used for researchers and/or senior graduate students in the areas of probability, control theory, mathematical finance, and other related fields.

Stochastic Modeling and Control

Ivan Ivanov
Stochastic Modeling and Control Book PDF

Author : Ivan Ivanov
Publisher : BoD – Books on Demand
Page : 288 pages
File Size : 41,5 Mb
Release : 2012-11-28
Category : Mathematics
ISBN : 9789535108306

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Stochastic Modeling and Control by Ivan Ivanov Pdf

Stochastic control plays an important role in many scientific and applied disciplines including communications, engineering, medicine, finance and many others. It is one of the effective methods being used to find optimal decision-making strategies in applications. The book provides a collection of outstanding investigations in various aspects of stochastic systems and their behavior. The book provides a self-contained treatment on practical aspects of stochastic modeling and calculus including applications drawn from engineering, statistics, and computer science. Readers should be familiar with basic probability theory and have a working knowledge of stochastic calculus. PhD students and researchers in stochastic control will find this book useful.

Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications

Rene Carmona
Lectures on BSDEs Stochastic Control and Stochastic Differential Games with Financial Applications Book PDF

Author : Rene Carmona
Publisher : SIAM
Page : 265 pages
File Size : 42,9 Mb
Release : 2016-02-18
Category : Mathematics
ISBN : 9781611974249

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Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications by Rene Carmona Pdf

The goal of this textbook is to introduce students to the stochastic analysis tools that play an increasing role in the probabilistic approach to optimization problems, including stochastic control and stochastic differential games. While optimal control is taught in many graduate programs in applied mathematics and operations research, the author was intrigued by the lack of coverage of the theory of stochastic differential games. This is the first title in SIAM?s Financial Mathematics book series and is based on the author?s lecture notes. It will be helpful to students who are interested in stochastic differential equations (forward, backward, forward-backward); the probabilistic approach to stochastic control (dynamic programming and the stochastic maximum principle); and mean field games and control of McKean?Vlasov dynamics. The theory is illustrated by applications to models of systemic risk, macroeconomic growth, flocking/schooling, crowd behavior, and predatory trading, among others.

Scientific and Technical Aerospace Reports

Anonim
Scientific and Technical Aerospace Reports Book PDF

Author : Anonim
Publisher : Unknown
Page : 748 pages
File Size : 54,5 Mb
Release : 1984
Category : Aeronautics
ISBN : UFL:31262082080416

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Scientific and Technical Aerospace Reports by Anonim Pdf

Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.

Deterministic and Stochastic Optimal Control and Inverse Problems

Baasansuren Jadamba,Akhtar A. Khan,Stanisław Migórski,Miguel Sama
Deterministic and Stochastic Optimal Control and Inverse Problems Book PDF

Author : Baasansuren Jadamba,Akhtar A. Khan,Stanisław Migórski,Miguel Sama
Publisher : CRC Press
Page : 378 pages
File Size : 52,6 Mb
Release : 2021-12-15
Category : Computers
ISBN : 9781000511758

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Deterministic and Stochastic Optimal Control and Inverse Problems by Baasansuren Jadamba,Akhtar A. Khan,Stanisław Migórski,Miguel Sama Pdf

Inverse problems of identifying parameters and initial/boundary conditions in deterministic and stochastic partial differential equations constitute a vibrant and emerging research area that has found numerous applications. A related problem of paramount importance is the optimal control problem for stochastic differential equations. This edited volume comprises invited contributions from world-renowned researchers in the subject of control and inverse problems. There are several contributions on optimal control and inverse problems covering different aspects of the theory, numerical methods, and applications. Besides a unified presentation of the most recent and relevant developments, this volume also presents some survey articles to make the material self-contained. To maintain the highest level of scientific quality, all manuscripts have been thoroughly reviewed.

Deterministic and Stochastic Optimal Control

Wendell H. Fleming,Raymond W. Rishel
Deterministic and Stochastic Optimal Control Book PDF

Author : Wendell H. Fleming,Raymond W. Rishel
Publisher : Springer Science & Business Media
Page : 231 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461263807

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Deterministic and Stochastic Optimal Control by Wendell H. Fleming,Raymond W. Rishel Pdf

This book may be regarded as consisting of two parts. In Chapters I-IV we pre sent what we regard as essential topics in an introduction to deterministic optimal control theory. This material has been used by the authors for one semester graduate-level courses at Brown University and the University of Kentucky. The simplest problem in calculus of variations is taken as the point of departure, in Chapter I. Chapters II, III, and IV deal with necessary conditions for an opti mum, existence and regularity theorems for optimal controls, and the method of dynamic programming. The beginning reader may find it useful first to learn the main results, corollaries, and examples. These tend to be found in the earlier parts of each chapter. We have deliberately postponed some difficult technical proofs to later parts of these chapters. In the second part of the book we give an introduction to stochastic optimal control for Markov diffusion processes. Our treatment follows the dynamic pro gramming method, and depends on the intimate relationship between second order partial differential equations of parabolic type and stochastic differential equations. This relationship is reviewed in Chapter V, which may be read inde pendently of Chapters I-IV. Chapter VI is based to a considerable extent on the authors' work in stochastic control since 1961. It also includes two other topics important for applications, namely, the solution to the stochastic linear regulator and the separation principle.