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Author: Khanh D. Pham Publisher: Springer Science & Business Media ISBN: 1461450780 Category : Mathematics Languages : en Pages : 157
Book Description
Linear-Quadratic Controls in Risk-Averse Decision Making cuts across control engineering (control feedback and decision optimization) and statistics (post-design performance analysis) with a common theme: reliability increase seen from the responsive angle of incorporating and engineering multi-level performance robustness beyond the long-run average performance into control feedback design and decision making and complex dynamic systems from the start. This monograph provides a complete description of statistical optimal control (also known as cost-cumulant control) theory. In control problems and topics, emphasis is primarily placed on major developments attained and explicit connections between mathematical statistics of performance appraisals and decision and control optimization. Chapter summaries shed light on the relevance of developed results, which makes this monograph suitable for graduate-level lectures in applied mathematics and electrical engineering with systems-theoretic concentration, elective study or a reference for interested readers, researchers, and graduate students who are interested in theoretical constructs and design principles for stochastic controlled systems.
Author: Paolo Vitale Publisher: ISBN: Category : Languages : en Pages : 42
Book Description
We discuss how Whittle's (Whittle, 1990) approach to risk-sensitive optimal control problems can be applied in economics and finance. We show how his analysis of the class of Linear Exponential Quadratic Gaussian problems can be extended to accommodate time-discounting, while preserving its simple and general recursive solutions. We apply Whittle's methodology investigating two specific problems in financial economics and monetary policy.
Author: Khanh D. Pham Publisher: Springer Science & Business Media ISBN: 1461450780 Category : Mathematics Languages : en Pages : 157
Book Description
Linear-Quadratic Controls in Risk-Averse Decision Making cuts across control engineering (control feedback and decision optimization) and statistics (post-design performance analysis) with a common theme: reliability increase seen from the responsive angle of incorporating and engineering multi-level performance robustness beyond the long-run average performance into control feedback design and decision making and complex dynamic systems from the start. This monograph provides a complete description of statistical optimal control (also known as cost-cumulant control) theory. In control problems and topics, emphasis is primarily placed on major developments attained and explicit connections between mathematical statistics of performance appraisals and decision and control optimization. Chapter summaries shed light on the relevance of developed results, which makes this monograph suitable for graduate-level lectures in applied mathematics and electrical engineering with systems-theoretic concentration, elective study or a reference for interested readers, researchers, and graduate students who are interested in theoretical constructs and design principles for stochastic controlled systems.
Author: Khanh D. Pham Publisher: Springer ISBN: 3319087053 Category : Mathematics Languages : en Pages : 222
Book Description
Providing readers with a detailed examination of resilient controls in risk-averse decision, this monograph is aimed toward researchers and graduate students in applied mathematics and electrical engineering with a systems-theoretic concentration. This work contains a timely and responsive evaluation of reforms on the use of asymmetry or skewness pertaining to the restrictive family of quadratic costs that have been appeared in various scholarly forums. Additionally, the book includes a discussion of the current and ongoing efforts in the usage of risk, dynamic game decision optimization and disturbance mitigation techniques with output feedback measurements tailored toward the worst-case scenarios. This work encompasses some of the current changes across uncertainty quantification, stochastic control communities, and the creative efforts that are being made to increase the understanding of resilient controls. Specific considerations are made in this book for the application of decision theory to resilient controls of the linear-quadratic class of stochastic dynamical systems. Each of these topics are examined explicitly in several chapters. This monograph also puts forward initiatives to reform both control decisions with risk consequences and correct-by-design paradigms for performance reliability associated with the class of stochastic linear dynamical systems with integral quadratic costs and subject to network delays, control and communication constraints.
Author: Peter Whittle Publisher: ISBN: Category : Mathematics Languages : en Pages : 266
Book Description
The two major themes of this book are risk-sensitive control and path-integral or Hamiltonian formulation. It covers risk-sensitive certainty-equivalence principles, the consequent extension of the conventional LQG treatment and the path-integral formulation.
Author: Jianing Yao Publisher: ISBN: Category : Languages : en Pages : 86
Book Description
This work analyzes an optimal control problem for which the performance is measured by a dynamic risk measure. While dynamic risk measures in discrete-time and the control problems associated are well understood, the continuous-time framework brings great challenges both in theory and practice. This study addresses modeling, numerical schemes and applications. In the first part, we focus on the formulation of a risk-averse control problem. Specifically, we make use of a decoupled forward-backward system of stochastic differential equations to evaluate a fixed policy: the forward stochastic differential equation (SDE) characterizes the evolution of states, and the backward stochastic differential equation (BSDE) does the risk evaluation at any instant of time. Relying on the Markovian structure of the system, we obtain the corresponding dynamic programming equation via weak formulation and strong formulation; in the meanwhile, the risk-averse Hamilton-Jacobi-Bellman equation and its verification are derived under suitable assumptions. In the second part, the main thrust is to find a convergent numerical method to solve the system in discrete-time setting. Specifically, we construct a piecewise-constant Markovian control to show its arbitrarily closeness to the optimal control. The results heavily relies on the regularity of the solution to generalized Hamilton-Jacobi-Bellman PDE. In the third part, we propose a numerical method for risk evaluation defined by BSDE. Using dual representation of the risk measure, we converted risk valuation to a stochastic control problem, where the control is the Radon-Nikodym derivative process. The optimality conditions of such control problem enables us to use a piecewise-constant density (control) to arrive at a close approximation on a short interval. Then, the Bellman principle extends the approximation to any finite time horizon problem. Lastly, we give a financial application in risk management in conjunction with nested simulation.
Author: Jingrui Sun Publisher: Springer Nature ISBN: 3030209229 Category : Mathematics Languages : en Pages : 129
Book Description
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: Goong Chen Publisher: CRC Press ISBN: 9780849380754 Category : Business & Economics Languages : en Pages : 404
Book Description
Linear Stochastic Control Systems presents a thorough description of the mathematical theory and fundamental principles of linear stochastic control systems. Both continuous-time and discrete-time systems are thoroughly covered. Reviews of the modern probability and random processes theories and the Itô stochastic differential equations are provided. Discrete-time stochastic systems theory, optimal estimation and Kalman filtering, and optimal stochastic control theory are studied in detail. A modern treatment of these same topics for continuous-time stochastic control systems is included. The text is written in an easy-to-understand style, and the reader needs only to have a background of elementary real analysis and linear deterministic systems theory to comprehend the subject matter. This graduate textbook is also suitable for self-study, professional training, and as a handy research reference. Linear Stochastic Control Systems is self-contained and provides a step-by-step development of the theory, with many illustrative examples, exercises, and engineering applications.
Author: Khanh D. Pham
Author: Paolo Vitale
Author: Khanh D. Pham
Author: Darinka Dentcheva
Author: Khanh D. Pham
Author: Peter Whittle
Author: Jianing Yao
Author: Jingrui Sun
Author: Goong Chen
Author: 
Author: Arthur E. Bryson