Download or read book Controlled Markov processes and viscosity solutions of nonlinear evolution written by Wendell H. Fleming and published by Edizioni della Normale. This book was released on 1988-10-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on a series of lectures delivered at the Scuola Normale Superiore in March 1986. They are intended to explore some connections between the theory of control of Markov stochastic processes and certain classes of nonlinear evolution equations. These connections arise by considering the dynamic programming equation associated with a stochastic control problem. Particular attention is given to controlled Markov diffusion processes on finite dimensional Euclidean space. In that case, the dynamic programming equation is a nonlinear partial differential equation of second order elliptic or parabolic type. For deterministic control the dynamic programming equation reduces to first order. From the viewpoint of nonlinear evolution equations, the interest is in whether one can find some stochastic control problem for which the given evolution equation is the dynamic programming equation. Classical solutions to first order or degenerate second order elliptic/parabolic equations with given boundary Cauchy data do not usually exist. One must instead consider generalized solutions. Viscosity solutions methods have substantially extended the theory.

Download or read book Controlled Markov Processes and Viscosity Solutions written by Wendell H. Fleming and published by Springer Science & Business Media. This book was released on 2006-02-04 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.

Download or read book Controlled Markov Processes and Viscosity Solutions written by Wendell Helms Fleming and published by . This book was released on 2006 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. The authors approach stochastic control problems by the method of dynamic programming. The text provides an introduction to dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. A new Chapter X gives an introduction to the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets. Chapter VI of the First Edition has been completely rewritten, to emphasize the relationships between logarithmic transformations and risk sensitivity. A new Chapter XI gives a concise introduction to two-controller, zero-sum differential games. Also covered are controlled Markov diffusions and viscosity solutions of Hamilton-Jacobi-Bellman equations. The authors have tried, through illustrative examples and selective material, to connect stochastic control theory with other mathematical areas (e.g. large deviations theory) and with applications to engineering, physics, management, and finance.; In this Second Edition, new material on applications to mathematical finance has been added. Concise introductions to risk-sensitive control theory, nonlinear H-infinity control and differential games are also included.

Download or read book Controlled Markov Processes and Viscosity Solution of Nonlinear Evolution Equations written by Wendell Helms Fleming and published by . This book was released on 1986 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Backward Stochastic Differential Equations written by N El Karoui and published by CRC Press. This book was released on 1997-01-17 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Viscosity Solutions and Applications written by Martino Bardi and published by Springer. This book was released on 2006-11-13 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume comprises five extended surveys on the recent theory of viscosity solutions of fully nonlinear partial differential equations, and some of its most relevant applications to optimal control theory for deterministic and stochastic systems, front propagation, geometric motions and mathematical finance. The volume forms a state-of-the-art reference on the subject of viscosity solutions, and the authors are among the most prominent specialists. Potential readers are researchers in nonlinear PDE's, systems theory, stochastic processes.

Download or read book Probabilistic and Statistical Aspects of Quantum Theory written by Alexander S. Holevo and published by Springer Science & Business Media. This book was released on 2011-05-05 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to aspects of the foundations of quantum mechanics in which probabilistic and statistical concepts play an essential role. The main part of the book concerns the quantitative statistical theory of quantum measurement, based on the notion of positive operator-valued measures. During the past years there has been substantial progress in this direction, stimulated to a great extent by new applications such as Quantum Optics, Quantum Communication and high-precision experiments. The questions of statistical interpretation, quantum symmetries, theory of canonical commutation relations and Gaussian states, uncertainty relations as well as new fundamental bounds concerning the accuracy of quantum measurements, are discussed in this book in an accessible yet rigorous way. Compared to the first edition, there is a new Supplement devoted to the hidden variable issue. Comments and the bibliography have also been extended and updated.

Download or read book Stochastic Analysis Control Optimization and Applications written by William M. McEneaney and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: In view of Professor Wendell Fleming's many fundamental contributions, his profound influence on the mathematical and systems theory communi ties, his service to the profession, and his dedication to mathematics, we have invited a number of leading experts in the fields of control, optimiza tion, and stochastic systems to contribute to this volume in his honor on the occasion of his 70th birthday. These papers focus on various aspects of stochastic analysis, control theory and optimization, and applications. They include authoritative expositions and surveys as well as research papers on recent and important issues. The papers are grouped according to the following four major themes: (1) large deviations, risk sensitive and Hoc control, (2) partial differential equations and viscosity solutions, (3) stochastic control, filtering and parameter esti mation, and (4) mathematical finance and other applications. We express our deep gratitude to all of the authors for their invaluable contributions, and to the referees for their careful and timely reviews. We thank Harold Kushner for having graciously agreed to undertake the task of writing the foreword. Particular thanks go to H. Thomas Banks for his help, advice and suggestions during the entire preparation process, as well as for the generous support of the Center for Research in Scientific Computation. The assistance from the Birkhauser professional staff is also greatly appreciated.

Download or read book Stochastic Analysis and Applications in Physics written by Ana Isabel Cardoso and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute, Funchal, Madeira, Portugal, August 6--19, 1993

Download or read book Novel Methods in Computational Finance written by Matthias Ehrhardt and published by Springer. This book was released on 2017-09-19 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the state-of-the-art and open problems in computational finance. It presents a collection of research outcomes and reviews of the work from the STRIKE project, an FP7 Marie Curie Initial Training Network (ITN) project in which academic partners trained early-stage researchers in close cooperation with a broader range of associated partners, including from the private sector. The aim of the project was to arrive at a deeper understanding of complex (mostly nonlinear) financial models and to develop effective and robust numerical schemes for solving linear and nonlinear problems arising from the mathematical theory of pricing financial derivatives and related financial products. This was accomplished by means of financial modelling, mathematical analysis and numerical simulations, optimal control techniques and validation of models. In recent years the computational complexity of mathematical models employed in financial mathematics has witnessed tremendous growth. Advanced numerical techniques are now essential to the majority of present-day applications in the financial industry. Special attention is devoted to a uniform methodology for both testing the latest achievements and simultaneously educating young PhD students. Most of the mathematical codes are linked into a novel computational finance toolbox, which is provided in MATLAB and PYTHON with an open access license. The book offers a valuable guide for researchers in computational finance and related areas, e.g. energy markets, with an interest in industrial mathematics.

Download or read book S gaku Expositions written by and published by . This book was released on 1996 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book OPTIMIZATION AND OPERATIONS RESEARCH Volume III written by Ulrich Derigs and published by EOLSS Publications. This book was released on 2009-02-09 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization and Operations Research is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme on Optimization and Operations Research is organized into six different topics which represent the main scientific areas of the theme: 1. Fundamentals of Operations Research; 2. Advanced Deterministic Operations Research; 3. Optimization in Infinite Dimensions; 4. Game Theory; 5. Stochastic Operations Research; 6. Decision Analysis, which are then expanded into multiple subtopics, each as a chapter. These four volumes are aimed at the following five major target audiences: University and College students Educators, Professional Practitioners, Research Personnel and Policy Analysts, Managers, and Decision Makers and NGOs.

Download or read book Stochastic Control Theory written by Makiko Nisio and published by Springer. This book was released on 2014-11-27 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems. First we consider completely observable control problems with finite horizons. Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton–Jacobi–Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory. When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise. This problem is treated in the same frameworks, via the nonlinear semigroup. Its results are applicable to the American option price problem. Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-max principle, to be precise). Using semi-discretization arguments, we construct the nonlinear semigroups whose generators provide lower and upper Isaacs equations. Concerning partially observable control problems, we refer to stochastic parabolic equations driven by colored Wiener noises, in particular, the Zakai equation. The existence and uniqueness of solutions and regularities as well as Itô's formula are stated. A control problem for the Zakai equations has a nonlinear semigroup whose generator provides the HJB equation on a Banach space. The value function turns out to be a unique viscosity solution for the HJB equation under mild conditions. This edition provides a more generalized treatment of the topic than does the earlier book Lectures on Stochastic Control Theory (ISI Lecture Notes 9), where time-homogeneous cases are dealt with. Here, for finite time-horizon control problems, DPP was formulated as a one-parameter nonlinear semigroup, whose generator provides the HJB equation, by using a time-discretization method. The semigroup corresponds to the value function and is characterized as the envelope of Markovian transition semigroups of responses for constant control processes. Besides finite time-horizon controls, the book discusses control-stopping problems in the same frameworks.

Download or read book Markov Processes Feller Semigroups and Evolution Equations written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Recent Developments in Nonlinear Partial Differential Equations written by Donatella Danielli and published by American Mathematical Soc.. This book was released on 2007 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains research and expository articles based on talks presented at the 2nd Symposium on Analysis and PDEs, held at Purdue University. The Symposium focused on topics related to the theory and applications of nonlinear partial differential equations that are at the forefront of current international research. Papers in this volume provide a comprehensive account of many of the recent developments in the field. The topics featured in this volume include: kinetic formulations of nonlinear PDEs; recent unique continuation results and their applications; concentrations and constrained Hamilton-Jacobi equations; nonlinear Schrodinger equations; quasiminimal sets for Hausdorff measures; Schrodinger flows into Kahler manifolds; and parabolic obstacle problems with applications to finance. The clear and concise presentation in many articles makes this volume suitable for both researchers and graduate students.

Download or read book Stochastic Analysis and Applications written by A.B. Cruzeiro and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the end of the summer 1989, an international conference on stochastic analysis and related topics was held for the first time in Lisbon (Portu gal). This meeting was made possible with the help of INIC and JNICT, two organizations devoted to the encouragement of scientific research in Portugal. The meeting was interdiciplinary since mathematicians and mathematical physicists from around the world were invited to present their recent works involving probability theory, analysis, geometry and physics, a wide area of cross fertilization in recent years. Portuguese scientific research is expanding fast, these days, faster, some times, than the relevant academic structures. The years to come will be determinant for the orientation of those young Portuguese willing to take an active part in the international scientific community. Lisbon's summer 89 meeting should initiate a new Iberic tradition, attrac tive both for these researchers to be and, of course, for the selected guests. Judging by the quality of contributions collected here, it is not unrealistic to believe that a tradition of "southern randomness" may well be established.

Download or read book Mathematics of Operations Research written by and published by . This book was released on 1990 with total page 892 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles of mathematical interest as well as operations research and management science.