Optimal Stochastic Control Stochastic Target Problems And Backward Sde

Author : Nizar Touzi
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 45,7 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.​

Author : Springer
Publisher : Unknown
Page : 226 pages
File Size : 44,5 Mb
Release : 2012-09-01
Category : Electronic
ISBN : 1461442877

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Optimal Stochastic Control, Stochastic Target Problems, and Backward Sde by Springer Pdf

Author : Jingrui Sun,Jiongmin Yong
Publisher : Springer Nature
Page : 129 pages
File Size : 42,9 Mb
Release : 2020-06-29
Category : Mathematics
ISBN : 9783030209223

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Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions 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 the results in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, it precisely identifies, for the first time, the interconnections between three well-known, relevant issues – the existence of optimal controls, solvability of the optimality system, and solvability of the associated Riccati equation. 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.

Author : Jianfeng Zhang
Publisher : Springer
Page : 388 pages
File Size : 43,5 Mb
Release : 2017-08-22
Category : Mathematics
ISBN : 9781493972562

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Backward Stochastic Differential Equations by Jianfeng Zhang Pdf

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.

Author : Guangchen Wang,Zhen Wu,Jie Xiong
Publisher : Springer
Page : 116 pages
File Size : 43,5 Mb
Release : 2018-05-16
Category : Mathematics
ISBN : 9783319790398

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An Introduction to Optimal Control of FBSDE with Incomplete Information by Guangchen Wang,Zhen Wu,Jie Xiong Pdf

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.

Author : Rene Carmona
Publisher : SIAM
Page : 263 pages
File Size : 41,5 Mb
Release : 2016-02-18
Category : Mathematics
ISBN : 9781611974232

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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.

Author : Qi Lü,Xu Zhang
Publisher : Springer Nature
Page : 592 pages
File Size : 47,8 Mb
Release : 2021-10-19
Category : Science
ISBN : 9783030823313

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Mathematical Control Theory for Stochastic Partial Differential Equations by Qi Lü,Xu Zhang Pdf

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.

Author : Pablo Azcue,Nora Muler
Publisher : Springer
Page : 146 pages
File Size : 43,6 Mb
Release : 2014-06-19
Category : Mathematics
ISBN : 9781493909957

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Stochastic Optimization in Insurance by Pablo Azcue,Nora Muler Pdf

The main purpose of the book is to show how a viscosity approach can be used to tackle control problems in insurance. The problems covered are the maximization of survival probability as well as the maximization of dividends in the classical collective risk model. The authors consider the possibility of controlling the risk process by reinsurance as well as by investments. They show that optimal value functions are characterized as either the unique or the smallest viscosity solution of the associated Hamilton-Jacobi-Bellman equation; they also study the structure of the optimal strategies and show how to find them. The viscosity approach was widely used in control problems related to mathematical finance but until quite recently it was not used to solve control problems related to actuarial mathematical science. This book is designed to familiarize the reader on how to use this approach. The intended audience is graduate students as well as researchers in this area.

Author : Jingrui Sun,Jiongmin Yong
Publisher : Springer Nature
Page : 138 pages
File Size : 46,8 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.

Author : N El Karoui,Laurent Mazliak
Publisher : CRC Press
Page : 236 pages
File Size : 54,8 Mb
Release : 1997-01-17
Category : Mathematics
ISBN : 0582307333

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Backward Stochastic Differential Equations by N El Karoui,Laurent Mazliak Pdf

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.

Author : Stefania Ugolini,Marco Fuhrman,Elisa Mastrogiacomo,Paola Morando,Barbara Rüdiger
Publisher : Springer Nature
Page : 273 pages
File Size : 49,6 Mb
Release : 2022-02-09
Category : Mathematics
ISBN : 9783030874322

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Geometry and Invariance in Stochastic Dynamics by Stefania Ugolini,Marco Fuhrman,Elisa Mastrogiacomo,Paola Morando,Barbara Rüdiger Pdf

This book grew out of the Random Transformations and Invariance in Stochastic Dynamics conference held in Verona from the 25th to the 28th of March 2019 in honour of Sergio Albeverio. It presents the new area of studies concerning invariance and symmetry properties of finite and infinite dimensional stochastic differential equations.This area constitutes a natural, much needed, extension of the theory of classical ordinary and partial differential equations, where the reduction theory based on symmetry and invariance of such classical equations has historically proved to be very important both for theoretical and numerical studies and has given rise to important applications. The purpose of the present book is to present the state of the art of the studies on stochastic systems from this point of view, present some of the underlying fundamental ideas and methods involved, and to outline the main lines for future developments. The main focus is on bridging the gap between deterministic and stochastic approaches, with the goal of contributing to the elaboration of a unified theory that will have a great impact both from the theoretical point of view and the point of view of applications. The reader is a mathematician or a theoretical physicist. The main discipline is stochastic analysis with profound ideas coming from Mathematical Physics and Lie’s Group Geometry. While the audience consists essentially of academicians, the reader can also be a practitioner with Ph.D., who is interested in efficient stochastic modelling.

Author : Alain Bensoussan
Publisher : Springer
Page : 547 pages
File Size : 54,6 Mb
Release : 2018-05-23
Category : Mathematics
ISBN : 9783319754567

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Estimation and Control of Dynamical Systems by Alain Bensoussan Pdf

This book provides a comprehensive presentation of classical and advanced topics in estimation and control of dynamical systems with an emphasis on stochastic control. Many aspects which are not easily found in a single text are provided, such as connections between control theory and mathematical finance, as well as differential games. The book is self-contained and prioritizes concepts rather than full rigor, targeting scientists who want to use control theory in their research in applied mathematics, engineering, economics, and management science. Examples and exercises are included throughout, which will be useful for PhD courses and graduate courses in general. Dr. Alain Bensoussan is Lars Magnus Ericsson Chair at UT Dallas and Director of the International Center for Decision and Risk Analysis which develops risk management research as it pertains to large-investment industrial projects that involve new technologies, applications and markets. He is also Chair Professor at City University Hong Kong.

Author : Baasansuren Jadamba,Akhtar A. Khan,Stanisław Migórski,Miguel Sama
Publisher : CRC Press
Page : 378 pages
File Size : 44,9 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.

Author : Uffe Høgsbro Thygesen
Publisher : CRC Press
Page : 381 pages
File Size : 55,6 Mb
Release : 2023-06-15
Category : Mathematics
ISBN : 9781000884999

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Stochastic Differential Equations for Science and Engineering by Uffe Høgsbro Thygesen Pdf

Stochastic Differential Equations for Science and Engineering is aimed at students at the M.Sc. and PhD level. The book describes the mathematical construction of stochastic differential equations with a level of detail suitable to the audience, while also discussing applications to estimation, stability analysis, and control. The book includes numerous examples and challenging exercises. Computational aspects are central to the approach taken in the book, so the text is accompanied by a repository on GitHub containing a toolbox in R which implements algorithms described in the book, code that regenerates all figures, and solutions to exercises. Features: Contains numerous exercises, examples, and applications Suitable for science and engineering students at Master’s or PhD level Thorough treatment of the mathematical theory combined with an accessible treatment of motivating examples GitHub repository available at: https://github.com/Uffe-H-Thygesen/SDEbook and https://github.com/Uffe-H-Thygesen/SDEtools

Author : Gennadii E. Kolosov
Publisher : CRC Press
Page : 424 pages
File Size : 52,5 Mb
Release : 1999-06-01
Category : Technology & Engineering
ISBN : 0824775376

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Optimal Design of Control Systems by Gennadii E. Kolosov Pdf

"Covers design methods for optimal (or quasioptimal) control algorithms in the form of synthesis for deterministic and stochastic dynamical systems-with applications in aerospace, robotic, and servomechanical technologies. Providing new results on exact and approximate solutions of optimal control problems."