Approximations and Computational Methods for Optimal Stopping and Stochastic Impulsive Control Problems PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Approximations and Computational Methods for Optimal Stopping and Stochastic Impulsive Control Problems PDF full book. Access full book title Approximations and Computational Methods for Optimal Stopping and Stochastic Impulsive Control Problems by Harold Joseph Kushner. Download full books in PDF and EPUB format.
Author: Harold Joseph Kushner
Publisher:
ISBN:
Category : Control theory
Languages : en
Pages : 33
Get Book Here
Book Description
The paper treats a computational method for the Optimal Stopping and Stochastic Impulsive Control problem for a diffusion. In the latter problem control acts only intermittently since there is a basic positive 'transaction' cost to be paid at each instant that the control acts. For each h> 0, a controlled Markov chain is constructed, whose continuous time interpolations are a natural approximation to the diffusion, for both the optimal stopping and impulsive control situations. The solutions to the optimal stopping and impulsive control problems for the chains are relatively easy to obtain by using standard procedures, and they converge to the solutions of the corresponding problems for the diffusion models as h nears 0.
Author: Harold Joseph Kushner
Publisher:
ISBN:
Category : Control theory
Languages : en
Pages : 33
Get Book Here
Book Description
The paper treats a computational method for the Optimal Stopping and Stochastic Impulsive Control problem for a diffusion. In the latter problem control acts only intermittently since there is a basic positive 'transaction' cost to be paid at each instant that the control acts. For each h> 0, a controlled Markov chain is constructed, whose continuous time interpolations are a natural approximation to the diffusion, for both the optimal stopping and impulsive control situations. The solutions to the optimal stopping and impulsive control problems for the chains are relatively easy to obtain by using standard procedures, and they converge to the solutions of the corresponding problems for the diffusion models as h nears 0.
Author: Harold Kushner
Publisher: Springer Science & Business Media
ISBN: 1468404415
Category : Science
Languages : en
Pages : 436
Get Book Here
Book Description
This book is concerned with numerical methods for stochastic control and optimal stochastic control problems. The random process models of the controlled or uncontrolled stochastic systems are either diffusions or jump diffusions. Stochastic control is a very active area of research and new prob lem formulations and sometimes surprising applications appear regularly. We have chosen forms of the models which cover the great bulk of the for mulations of the continuous time stochastic control problems which have appeared to date. The standard formats are covered, but much emphasis is given to the newer and less well known formulations. The controlled process might be either stopped or absorbed on leaving a constraint set or upon first hitting a target set, or it might be reflected or "projected" from the boundary of a constraining set. In some of the more recent applications of the reflecting boundary problem, for example the so-called heavy traffic approximation problems, the directions of reflection are actually discontin uous. In general, the control might be representable as a bounded function or it might be of the so-called impulsive or singular control types. Both the "drift" and the "variance" might be controlled. The cost functions might be any of the standard types: Discounted, stopped on first exit from a set, finite time, optimal stopping, average cost per unit time over the infinite time interval, and so forth.
Author: Harold J. Kushner
Publisher:
ISBN:
Category :
Languages : en
Pages : 45
Get Book Here
Book Description
Stochastic control problems of either the optimal stopping or impulsive control type on diffusion models are considered, but there is also a continuously acting control. Various computationally convenient Markov chain approximations to the problems are developed, and it is shown that the costs for the sequence of approximations converge to the optimal cost for original problems.
Author: Kushner
Publisher: Academic Press
ISBN: 0080956386
Category : Computers
Languages : en
Pages : 263
Get Book Here
Book Description
Probability Methods for Approximations in Stochastic Control and for Elliptic Equations
Author: Harold Kushner
Publisher: Springer Science & Business Media
ISBN: 0817646213
Category : Science
Languages : en
Pages : 295
Get Book Here
Book Description
The Markov chain approximation methods are widely used for the numerical solution of nonlinear stochastic control problems in continuous time. This book extends the methods to stochastic systems with delays. The book is the first on the subject and will be of great interest to all those who work with stochastic delay equations and whose main interest is either in the use of the algorithms or in the mathematics. An excellent resource for graduate students, researchers, and practitioners, the work may be used as a graduate-level textbook for a special topics course or seminar on numerical methods in stochastic control.
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 892
Get Book Here
Book Description
Author: Harold J. Kushner
Publisher: Springer Science & Business Media
ISBN: 9780387951393
Category : Language Arts & Disciplines
Languages : en
Pages : 496
Get Book Here
Book Description
The required background is surveyed, and there is an extensive development of methods of approximation and computational algorithms. The book is written on two levels: algorithms and applications, and mathematical proofs. Thus, the ideas should be very accessible to a broad audience."--BOOK JACKET.
Author:
Publisher: Elsevier
ISBN: 0080529879
Category : Technology & Engineering
Languages : en
Pages : 363
Get Book Here
Book Description
Praise for Previous Volumes "This book will be a useful reference to control engineers and researchers. The papers contained cover well the recent advances in the field of modern control theory." -IEEE GROUP CORRESPONDENCE "This book will help all those researchers who valiantly try to keep abreast of what is new in the theory and practice of optimal control." -CONTROL
Author: David Šiška
Publisher:
ISBN:
Category :
Languages : en
Pages : 109
Get Book Here
Book Description
We study numerical approximations for the payoff function of the stochastic optimal stopping and control problem. It is known that the payoff function of the optimal stopping and control problem corresponds to the solution of a normalized Bellman PDE. The principal aim of this thesis is to study the rate at which finite difference approximations, derived from the normalized Bellman PDE, converge to the payoff function of the optimal stopping and control problem. We do this by extending results of N.V. Krylov from the Bellman equation to the normalized Bellman equation. To our best knowledge, until recently, no results about the rate of convergence of finite difference approximations to Bellman equations have been known. A major breakthrough has been made by N. V. Krylov. He proved rate of rate of convergence of tau 1/4 + h 1/2 where tau and h are the step sizes in time and space respectively. We will use the known idea of randomized stopping to give a direct proof showing that optimal stopping and control problems can be rewritten as pure optimal control problems by introducing a new control parameter and by allowing the reward and discounting functions to be unbounded in the control parameter. We extend important results of N. V. Krylov on the numerical solutions to the Bellman equations to the normalized Bellman equations associated with the optimal stopping of controlled diffusion processes. We obtain the same rate of convergence of tau1/4 + h1/2. This rate of convergence holds for finite difference schemes defined on a grid on the whole space [0, T]×Rd i.e. on a grid with infinitely many elements. This leads to the study of localization error, which arises when restricting the finite difference approximations to a cylindrical domain. As an application of our results, we consider an optimal stopping problem from mathematical finance: the pricing of American put option on multiple assets. We prove the rate of convergence of tau1/4 + h1/2 for the finite difference approximations.
Author: I.H. Mufti
Publisher: Springer Science & Business Media
ISBN: 3642859607
Category : Mathematics
Languages : en
Pages : 54
Get Book Here
Book Description
The purpose of this modest report is to present in a simplified manner some of the computational methods that have been developed in the last ten years for the solution of optimal control problems. Only those methods that are based on the minimum (maximum) principle of Pontriagin are discussed here. The autline of the report is as follows: In the first two sections a control problem of Bolza is formulated and the necessary conditions in the form of the minimum principle are given. The method of steepest descent and a conjugate gradient-method are dis cussed in Section 3. In the remaining sections, the successive sweep method, the Newton-Raphson method and the generalized Newton-Raphson method (also called quasilinearization method) ar~ presented from a unified approach which is based on the application of Newton Raphson approximation to the necessary conditions of optimality. The second-variation method and other shooting methods based on minimizing an error function are also considered. TABLE OF CONTENTS 1. 0 INTRODUCTION 1 2. 0 NECESSARY CONDITIONS FOR OPTIMALITY •••••••• 2 3. 0 THE GRADIENT METHOD 4 3. 1 Min H Method and Conjugate Gradient Method •. •••••••••. . . . ••••••. ••••••••. • 8 3. 2 Boundary Constraints •••••••••••. ••••. • 9 3. 3 Problems with Control Constraints ••. •• 15 4. 0 SUCCESSIVE SWEEP METHOD •••••••••••••••••••• 18 4. 1 Final Time Given Implicitly ••••. •••••• 22 5. 0 SECOND-VARIATION METHOD •••••••••••••••••••• 23 6. 0 SHOOTING METHODS ••••••••••••••••••••••••••• 27 6. 1 Newton-Raphson Method ••••••••••••••••• 27 6.
