Convex Stochastic Control and Conjugate Duality in a Problem of Unconstrained Utility Maximization Under a Regime Switching Model

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ISBN 13 :
Total Pages : 70 pages
Book Rating : 4.:/5 (926 download)

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Book Synopsis Convex Stochastic Control and Conjugate Duality in a Problem of Unconstrained Utility Maximization Under a Regime Switching Model by : Aaron Xin Situ

Download or read book Convex Stochastic Control and Conjugate Duality in a Problem of Unconstrained Utility Maximization Under a Regime Switching Model written by Aaron Xin Situ and published by . This book was released on 2015 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we examine a problem of convex stochastic optimal control applied to mathematical finance. The goal is to maximize the expected utility from wealth at close of trade (or terminal wealth) under a regime switching model. The presence of regime switching constitutes a definite challenge, and in order to keep the analysis tractable we therefore adopt a market model which is in other respects quite simple, and in particular does not involve margin payments, inter-temporal consumption or portfolio constraints. The asset prices will be modeled by classical Ito processes, and the market parameters will be dependent on the underlying Brownian Motion as well as a finite-state Markov Chain which represents the "regime switching" aspect of the market model. We use conjugate duality to construct a dual optimization problem and establish optimality relations between (putative) solutions of the dual and primal problems. We then apply these optimality relations to two specific types of utility functions, namely the power utility and logarithmic utility functions, and for these utility functions we obtain the optimal portfolios in completely explicit and implementable form.

Conjugate Duality and Optimization

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Publisher : SIAM
ISBN 13 : 0898710138
Total Pages : 82 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Conjugate Duality and Optimization by : R. Tyrrell Rockafellar

Download or read book Conjugate Duality and Optimization written by R. Tyrrell Rockafellar and published by SIAM. This book was released on 1974-01-01 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of duality in problems of optimization is developed in a setting of finite and infinite dimensional spaces using convex analysis. Applications to convex and nonconvex problems. Expository account containing many new results. (Author).

Conjugate Duality in Convex Optimization

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Publisher : Springer
ISBN 13 : 9783642049156
Total Pages : 164 pages
Book Rating : 4.0/5 (491 download)

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Book Synopsis Conjugate Duality in Convex Optimization by : Radu Ioan-Bot

Download or read book Conjugate Duality in Convex Optimization written by Radu Ioan-Bot and published by Springer. This book was released on 2011-03-03 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: The results presented in this book originate from the last decade research work of the author in the ?eld of duality theory in convex optimization. The reputation of duality in the optimization theory comes mainly from the major role that it plays in formulating necessary and suf?cient optimality conditions and, consequently, in generatingdifferent algorithmic approachesfor solving mathematical programming problems. The investigations made in this work prove the importance of the duality theory beyond these aspects and emphasize its strong connections with different topics in convex analysis, nonlinear analysis, functional analysis and in the theory of monotone operators. The ?rst part of the book brings to the attention of the reader the perturbation approach as a fundamental tool for developing the so-called conjugate duality t- ory. The classical Lagrange and Fenchel duality approaches are particular instances of this general concept. More than that, the generalized interior point regularity conditions stated in the past for the two mentioned situations turn out to be p- ticularizations of the ones given in this general setting. In our investigations, the perturbationapproachrepresentsthestartingpointforderivingnewdualityconcepts for several classes of convex optimization problems. Moreover, via this approach, generalized Moreau–Rockafellar formulae are provided and, in connection with them, a new class of regularity conditions, called closedness-type conditions, for both stable strong duality and strong duality is introduced. By stable strong duality we understand the situation in which strong duality still holds whenever perturbing the objective function of the primal problem with a linear continuous functional.

Duality in Vector Optimization

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Publisher : Springer Science & Business Media
ISBN 13 : 3642028861
Total Pages : 408 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Duality in Vector Optimization by : Radu Ioan Bot

Download or read book Duality in Vector Optimization written by Radu Ioan Bot and published by Springer Science & Business Media. This book was released on 2009-08-12 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. One chapter is exclusively consecrated to the scalar and vector Wolfe and Mond-Weir duality schemes.

Convex Duality for Finite-fuel Problems in Singular Stochastic Control

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Publisher :
ISBN 13 :
Total Pages : 40 pages
Book Rating : 4.:/5 (24 download)

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Book Synopsis Convex Duality for Finite-fuel Problems in Singular Stochastic Control by : Hang Zhu

Download or read book Convex Duality for Finite-fuel Problems in Singular Stochastic Control written by Hang Zhu and published by . This book was released on 1990 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Deterministic and Stochastic Optimal Control

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Publisher : Springer Science & Business Media
ISBN 13 : 1461263808
Total Pages : 231 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Deterministic and Stochastic Optimal Control by : Wendell H. Fleming

Download or read book Deterministic and Stochastic Optimal Control written by Wendell H. Fleming and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Duality for Nonconvex Approximation and Optimization

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Publisher : Springer Science & Business Media
ISBN 13 : 0387283951
Total Pages : 366 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Duality for Nonconvex Approximation and Optimization by : Ivan Singer

Download or read book Duality for Nonconvex Approximation and Optimization written by Ivan Singer and published by Springer Science & Business Media. This book was released on 2007-03-12 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of convex optimization has been constantly developing over the past 30 years. Most recently, many researchers have been studying more complicated classes of problems that still can be studied by means of convex analysis, so-called "anticonvex" and "convex-anticonvex" optimizaton problems. This manuscript contains an exhaustive presentation of the duality for these classes of problems and some of its generalization in the framework of abstract convexity. This manuscript will be of great interest for experts in this and related fields.

Deterministic and Stochastic Optimal Control and Inverse Problems

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Publisher : CRC Press
ISBN 13 : 1000511758
Total Pages : 378 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Deterministic and Stochastic Optimal Control and Inverse Problems by : Baasansuren Jadamba

Download or read book Deterministic and Stochastic Optimal Control and Inverse Problems written by Baasansuren Jadamba and published by CRC Press. This book was released on 2021-12-15 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Utility Maximization with Consumption Habit Formation in Incomplete Markets

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Publisher :
ISBN 13 :
Total Pages : 342 pages
Book Rating : 4.:/5 (799 download)

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Book Synopsis Utility Maximization with Consumption Habit Formation in Incomplete Markets by : Xiang Yu

Download or read book Utility Maximization with Consumption Habit Formation in Incomplete Markets written by Xiang Yu and published by . This book was released on 2012 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation studies a class of path-dependent stochastic control problems with applications to Finance. In particular, we solve the open problem of the continuous time expected utility maximization with addictive consumption habit formation in incomplete markets under two independent scenarios. In the first project, we study the continuous time utility optimization problem with consumption habit formation in general incomplete semimartingale financial markets. Introducing the set of auxiliary state processes and the modified dual space, we embed our original problem into an abstract time-separable utility maximization problem with a shadow random endowment on the product space [mathematic equation] We establish existence and uniqueness of the optimal solution using convex duality by defining the primal value function as depending on two variables, i.e., the initial wealth and the initial standard of living. We also provide market independent sufficient conditions both on the stochastic discounting processes of the habit formation process and on the utility function for the well-posedness of our original optimization problem. Under the same assumptions, we can carefully modify the classical proofs in the approach of convex duality analysis when the auxiliary dual process is not necessarily integrable. In the second project, we examine an example of the optimal investment and consumption problem with both habit-formation and partial observations in incomplete markets driven by Itô processes. The individual investor develops addictive consumption habits gradually while only observing the market stock prices but not the instantaneous rates of return, which follow an Ornstein-Uhlenbeck process. Applying the Kalman-Bucy filtering theorem and Dynamic Programming arguments, we solve the associated Hamilton-Jacobi-Bellman(HJB) equation fully explicitly for this path dependent stochastic control problem in the case of power utility preferences. We provide the optimal investment and consumption policy in explicit feedback form using rigorous verification arguments.

Conjugate Duality in Convex Optimization

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ISBN 13 :
Total Pages : 171 pages
Book Rating : 4.:/5 (624 download)

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Book Synopsis Conjugate Duality in Convex Optimization by : Radu Ioan Boţ

Download or read book Conjugate Duality in Convex Optimization written by Radu Ioan Boţ and published by . This book was released on 2008 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Duality in Stochastic Linear and Dynamic Programming

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Publisher : Springer Science & Business Media
ISBN 13 : 3642516971
Total Pages : 299 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Duality in Stochastic Linear and Dynamic Programming by : Willem K. Klein Haneveld

Download or read book Duality in Stochastic Linear and Dynamic Programming written by Willem K. Klein Haneveld and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Duality in Optimization and Variational Inequalities

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Publisher : Taylor & Francis
ISBN 13 : 9780415274791
Total Pages : 344 pages
Book Rating : 4.2/5 (747 download)

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Book Synopsis Duality in Optimization and Variational Inequalities by : C.j. Goh

Download or read book Duality in Optimization and Variational Inequalities written by C.j. Goh and published by Taylor & Francis. This book was released on 2002-05-10 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive volume covers a wide range of duality topics ranging from simple ideas in network flows to complex issues in non-convex optimization and multicriteria problems. In addition, it examines duality in the context of variational inequalities and vector variational inequalities, as generalizations to optimization. Duality in Optimization and Variational Inequalities is intended for researchers and practitioners of optimization with the aim of enhancing their understanding of duality. It provides a wider appreciation of optimality conditions in various scenarios and under different assumptions. It will enable the reader to use duality to devise more effective computational methods, and to aid more meaningful interpretation of optimization and variational inequality problems.

Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems

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Publisher : Springer Science & Business Media
ISBN 13 : 146124482X
Total Pages : 245 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems by : Harold Kushner

Download or read book Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems written by Harold Kushner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with several closely related topics concerning approxima tions and perturbations of random processes and their applications to some important and fascinating classes of problems in the analysis and design of stochastic control systems and nonlinear filters. The basic mathematical methods which are used and developed are those of the theory of weak con vergence. The techniques are quite powerful for getting weak convergence or functional limit theorems for broad classes of problems and many of the techniques are new. The original need for some of the techniques which are developed here arose in connection with our study of the particular applica tions in this book, and related problems of approximation in control theory, but it will be clear that they have numerous applications elsewhere in weak convergence and process approximation theory. The book is a continuation of the author's long term interest in problems of the approximation of stochastic processes and its applications to problems arising in control and communication theory and related areas. In fact, the techniques used here can be fruitfully applied to many other areas. The basic random processes of interest can be described by solutions to either (multiple time scale) Ito differential equations driven by wide band or state dependent wide band noise or which are singularly perturbed. They might be controlled or not, and their state values might be fully observable or not (e. g. , as in the nonlinear filtering problem).

Convex Duality for Epstein-Zin Stochastic Differential Utility

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Publisher :
ISBN 13 :
Total Pages : 25 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Convex Duality for Epstein-Zin Stochastic Differential Utility by : Anis Matoussi

Download or read book Convex Duality for Epstein-Zin Stochastic Differential Utility written by Anis Matoussi and published by . This book was released on 2016 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper introduces a dual problem to study a continuous-time consumption and investment problem with incomplete markets and Epstein-Zin stochastic differential utility. Duality between the primal and dual problems is established. Consequently the optimal strategy of this consumption and investment problem is identified without assuming several technical conditions on market model, utility specification, and agent's admissible strategy. Meanwhile the minimizer of the dual problem is identified as the utility gradient of the primal value and is economically interpreted as the "least favorable" completion of the market.

Introduction to Stochastic Control Theory

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Publisher : Courier Corporation
ISBN 13 : 0486445313
Total Pages : 322 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Introduction to Stochastic Control Theory by : Karl J. Åström

Download or read book Introduction to Stochastic Control Theory written by Karl J. Åström and published by Courier Corporation. This book was released on 2006-01-06 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unabridged republication of the edition published by Academic Press, 1970.

Duality Principles in Nonconvex Systems

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Publisher : Springer Science & Business Media
ISBN 13 : 9780792361459
Total Pages : 476 pages
Book Rating : 4.3/5 (614 download)

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Book Synopsis Duality Principles in Nonconvex Systems by : David Yang Gao

Download or read book Duality Principles in Nonconvex Systems written by David Yang Gao and published by Springer Science & Business Media. This book was released on 2000-01-31 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.

Stochastic Control and BSDEs in a Robust Utility Maximization Problem with an Entropic Penalty Term

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (14 download)

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Book Synopsis Stochastic Control and BSDEs in a Robust Utility Maximization Problem with an Entropic Penalty Term by : Giuliana Bordigoni

Download or read book Stochastic Control and BSDEs in a Robust Utility Maximization Problem with an Entropic Penalty Term written by Giuliana Bordigoni and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: