An Introduction To Optimal Control Of Fbsde With Incomplete Information

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An Introduction To Optimal Control Of Fbsde With Incomplete Information

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Author : Guangchen Wang
language : en
Publisher: Springer
Release Date : 2018-05-16

An Introduction To Optimal Control Of Fbsde With Incomplete Information written by Guangchen Wang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-16 with Mathematics categories.

This book focuses on maximum principle and verification theorem for incomplete information forward-backward stochastic differential equations (FBSDEs) and their applications in linear-quadratic optimal controls and mathematical finance. ​Lots of interesting phenomena arising from the area of mathematical finance can be described by FBSDEs. Optimal control problems of FBSDEs are theoretically important and practically relevant. A standard assumption in the literature is that the stochastic noises in the model are completely observed. However, this is rarely the case in real world situations. The optimal control problems under complete information are studied extensively. Nevertheless, very little is known about these problems when the information is not complete. The aim of this book is to fill this gap. This book is written in a style suitable for graduate students and researchers in mathematics and engineering with basic knowledge of stochastic process, optimal control and mathematical finance.

Mathematical Control Theory For Stochastic Partial Differential Equations

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Author : Qi Lü
language : en
Publisher: Springer Nature
Release Date : 2021-09-17

Mathematical Control Theory For Stochastic Partial Differential Equations written by Qi Lü and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-17 with Science categories.

This is the first book to systematically present control theory for stochastic distributed parameter systems, a comparatively new branch of mathematical control theory. The new phenomena and difficulties arising in the study of controllability and optimal control problems for this type of system are explained in detail. Interestingly enough, one has to develop new mathematical tools to solve some problems in this field, such as the global Carleman estimate for stochastic partial differential equations and the stochastic transposition method for backward stochastic evolution equations. In a certain sense, the stochastic distributed parameter control system is the most general control system in the context of classical physics. Accordingly, studying this field may also yield valuable insights into quantum control systems. A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.

Backward Stochastic Differential Equations

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Author : N El Karoui
language : en
Publisher: CRC Press
Release Date : 1997-01-17

Backward Stochastic Differential Equations written by N El Karoui and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-17 with Mathematics categories.

This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.

Probabilistic Theory Of Mean Field Games With Applications Ii

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Author : René Carmona
language : en
Publisher: Springer
Release Date : 2018-03-08

Probabilistic Theory Of Mean Field Games With Applications Ii written by René Carmona and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-08 with Mathematics categories.

This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume II tackles the analysis of mean field games in which the players are affected by a common source of noise. The first part of the volume introduces and studies the concepts of weak and strong equilibria, and establishes general solvability results. The second part is devoted to the study of the master equation, a partial differential equation satisfied by the value function of the game over the space of probability measures. Existence of viscosity and classical solutions are proven and used to study asymptotics of games with finitely many players. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.

Hidden Markov Models

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Author : Robert J Elliott
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-27

Hidden Markov Models written by Robert J Elliott and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-27 with Science categories.

As more applications are found, interest in Hidden Markov Models continues to grow. Following comments and feedback from colleagues, students and other working with Hidden Markov Models the corrected 3rd printing of this volume contains clarifications, improvements and some new material, including results on smoothing for linear Gaussian dynamics. In Chapter 2 the derivation of the basic filters related to the Markov chain are each presented explicitly, rather than as special cases of one general filter. Furthermore, equations for smoothed estimates are given. The dynamics for the Kalman filter are derived as special cases of the authors’ general results and new expressions for a Kalman smoother are given. The Chapters on the control of Hidden Markov Chains are expanded and clarified. The revised Chapter 4 includes state estimation for discrete time Markov processes and Chapter 12 has a new section on robust control.

Applied Stochastic Control Of Jump Diffusions

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Author : Bernt Øksendal
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-26

Applied Stochastic Control Of Jump Diffusions written by Bernt Øksendal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-26 with Mathematics categories.

Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.

Backward Stochastic Differential Equations

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Author : Jianfeng Zhang
language : en
Publisher: Springer
Release Date : 2017-08-22

Backward Stochastic Differential Equations written by Jianfeng Zhang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-22 with Mathematics categories.

This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.

Probabilistic Theory Of Mean Field Games With Applications I

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Author : René Carmona
language : en
Publisher: Springer
Release Date : 2018-03-01

Probabilistic Theory Of Mean Field Games With Applications I written by René Carmona and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-01 with Mathematics categories.

This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic mean field control problems. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.

Numerical Methods In Finance

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Author : René Carmona
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-03-23

Numerical Methods In Finance written by René Carmona and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-23 with Mathematics categories.

Numerical methods in finance have emerged as a vital field at the crossroads of probability theory, finance and numerical analysis. Based on presentations given at the workshop Numerical Methods in Finance held at the INRIA Bordeaux (France) on June 1-2, 2010, this book provides an overview of the major new advances in the numerical treatment of instruments with American exercises. Naturally it covers the most recent research on the mathematical theory and the practical applications of optimal stopping problems as they relate to financial applications. By extension, it also provides an original treatment of Monte Carlo methods for the recursive computation of conditional expectations and solutions of BSDEs and generalized multiple optimal stopping problems and their applications to the valuation of energy derivatives and assets. The articles were carefully written in a pedagogical style and a reasonably self-contained manner. The book is geared toward quantitative analysts, probabilists, and applied mathematicians interested in financial applications.

Foundations Of Computational Mathematics

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Author : Ronald A. DeVore
language : en
Publisher: Cambridge University Press
Release Date : 2001-05-17

Foundations Of Computational Mathematics written by Ronald A. DeVore and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-17 with Mathematics categories.

Collection of papers by leading researchers in computational mathematics, suitable for graduate students and researchers.