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Optimisation et contrôle stochastique appliqués à la finance = Optimization and stochastic control applied to finance
The objective and the originality of this book is to present the different aspects and methods used in the resolution of stochastic optimization problems with a view to more specific applications in finance: portfolio management, option hedging, optimal investment. . We have included some recent developments on the subject without seeking a priori the greatest generality. We wanted a gradual exposure of mathematical methods by first presenting the intuitive ideas and then precisely stating the results with full and detailed proofs.
Optimisation appliquée = Optimization applied
Presents the fundamental concepts of classical optimization and linear programming. In addition to a prologue and epilogue, the book includes a section on mathematical theory, covering matrix calculus and systems of linear equations and inequalities. It then deals with classical optimization, both constrained and unconstrained, linear programming, the simplex method, and the revised simplex method. The final chapters are devoted to duality, post-optimization and sensitivity analysis, as well as transportation problems. Emphasis is placed on explaining the methods presented and their applications. Numerous numerical examples drawn from various economic and social situations are provided.
Optimal Stopping Rules
Although three decades have passed since first publication of this book reprinted now as a result of popular demand, the content remains up-to-date and interesting for many researchers as is shown by the many references to it in current publications. The "ground floor" of Optimal Stopping Theory was constructed by A.Wald in his sequential analysis in connection with the testing of statistical hypotheses by non-traditional (sequential) methods. It was later discovered that these methods have, in idea, a close connection to the general theory of stochastic optimization for random processes.
Optimal Stopping and Free-Boundary Problems
The present monograph has the following particular aims: To present basic results (with proofs) of optimal stopping theory in both discrete and continuous time using both martingale and Mar- vian approaches; To select a seriesof concrete problems ofgeneral interest from the t- ory of probability, mathematical statistics, and mathematical ?nance that can be reformulated as problems of optimal stopping of stochastic processes and solved by reduction to free-boundary problems of real analysis (Stefan problems). The table of contents found below gives a clearer idea of the material included in the monograph. Credits and historical comments are given at the end of each chapter or section. The bibliography contains a material for further reading.
Optimal Production Planning for PCB Assembly
It is indisputable that printed circuit boards (PCBs) play a vital role in our daily life. With the ever-increasing applications of PCBs, one of the crucial ways to increase a PCB company’s competitiveness in terms of operation efficiency is to minimize the production time so that the products can be introduced to the market sooner. Optimal Production Planning for PCB Assembly is the first book to focus on the optimization of the PCB assembly line’s efficiency.
Optimal Domain and Integral Extension of Operators : Acting in Function Spaces
Operator theory and functional analysis have a long tradition, initially being guided by problems from mathematical physics and applied mathematics. Much of the work in Banach spaces from the 1930s onwards resulted from investigating how much real (and complex) variable function theory might be extended to fu- tions taking values in (function) spaces or operators acting in them. Many of the ?rst ideas in geometry, basis theory and the isomorphic theory of Banach spaces have vector measure-theoretic origins and can be credited (amongst others) to N. Dunford, I.M. Gelfand, B.J. Pettis and R.S. Phillips. Somewhat later came the penetrating contributions of A. Grothendieck, which have pervaded and influenced the shape of functional analysis and the theory of vector measures / integration ever since. Today, each of the areas of functional analysis/operator theory, Banach spaces, and vector measures/integration is a strong discipline in its own right. However, it is not always made clear that these areas grew up together as cousins and that they had, and still have, enormous in?uences on one another. One of the aims of this monograph is to reinforce and make transparent precisely this important point.
Optimal Control with Engineering Applications
Because the theoretical part of the book is based on the calculus of variations, the exposition is very transparent and requires mostly a trivial mathematical background. In the case of open-loop optimal control, this leads to Pontryagin’s Minimum Principle and, in the case of closed-loop optimal control, to the Hamilton-Jacobi-Bellman theory which exploits the principle of optimality. Many optimal control problems are solved completely in the body of the text. Furthermore, all of the exercise problems which appear at the ends of the chapters are sketched in the appendix. The book also covers some material that is not usually found in optimal control text books, namely, optimal control problems with non-scalar-valued performance criteria (with applications to optimal filtering) and Lukes’ method of approximatively-optimal control design.
Optimal Control of Constrained Piecewise Affine Systems
One of the most important and challenging problems in control is the derivation of systematic tools for the computation of controllers for constrained nonlinear systems that can guarantee closed-loop stability, feasibility, and optimality with respect to some performance index. This book focuses on the efficient and systematic computation of closed-form optimal controllers for the powerful class of fast-sampled constrained piecewise affine systems. These systems may exhibit rather complex behavior and are equivalent to many other hybrid system formalisms (combining continuous-valued dynamics with logic rules) reported in the literature. Furthermore, piecewise affine systems are a useful modeling tool that can capture general nonlinearities (e.g. by local approximation), constraints, saturations, switches, and other hybrid modeling phenomena. The first part of the book presents an introduction to the mathematical and control theoretical background material needed for the full understanding of the book.
Optics : Learning by Computing, with Examples Using Mathcad, Matlab, Mathematica, and Maple
It uses scripts from Maple, MathCad, Mathematica, and MATLAB provide a simulated laboratory where students can learn by exploration and discovery instead of passive absorption. The text covers all the standard topics of a traditional optics course, including: geometrical optics and aberration, interference and diffraction, coherence, Maxwell's equations, wave guides and propagating modes, blackbody radiation, atomic emission and lasers, optical properties of materials, Fourier transforms and FT spectroscopy, image formation, and holography. It contains step by step derivations of all basic formulas in geometrical, wave and Fourier optics.
Optical Scanning Holography with MATLAB
Optical scanning holography (OSH) is an emerging area of interest with many potential novel applications, such as 3-D pattern recognition, 3-D microscopy, 3-D cryptography, and 3-D optical remote sensing. Optical Scanning Holography with MATLAB® introduces readers to the latest advances of electronic (or digital) holography and succinctly covers the necessary mathematical background and wave optics that pertain to Fourier optics and holography. The reader is guided through modeling of the theory and applications utilizing MATLAB®. Optical scanning holography is explained in a manner that enables readers to begin implementing their own setups for novel OSH applications.
Oppositional Concepts in Computational Intelligence
This volume is a first attempt to bring together researchers who are inquiring into the complementary nature of systems and processes and, on the other hand, it provides some elementary components for a framework to establish a formalism for opposition-based computing. From a computational intelligence perspective, many successful opposition-based concepts have been in existence for a long time. It is not the authors intention to recast these existing methods, rather to elucidate that, while diverse, they all share the commonality of opposition - in one form or another, either implicitly or explicitly. Therefore they have attempted to provide rough guidelines to understand what makes concepts "oppositional.
Operator Theory, Analysis and Mathematical Physics
Contains lectures delivered by the participants of the international conference "Operator Theory, Analysis and Mathematical Physics" (OTAMP 2004), held at the Mathematical Research and Conference Center in Bedlewo near Poznan, Poland on July 6-11, 2004. The idea behind these lectures was to present interesting ramifications of operator methods in current research of mathematical physics. The main topics are functional models of non-selfadjoint operators, spectral properties of Dirac and Jacobi matrices, Dirichlet-to-Neumann techniques, Lyapunov exponents methods, and inverse spectral problems for quantum graphs.
Operations Research Proceedings 2007 ; Selected Papers of the Annual International Conference of the German Operations Research Society (GOR)
The symposium Operations Research 2007 was held from September 5-7, 2007 at the Saarland University in Saarbru ¨cken. This international conference is at the same time the annual meeting of the German - erations Research Society (GOR). The transition in Germany (and many other countries in Europe) from a production orientation to a service society combined with a continuous demographic change generated a need for intensi?ed Op- ations Research activities in this area. On that account this conference has been devoted to the role of Operations Research in the service industry. The links to Operations Research are manifold and include many di?erent topics which are particularly emphasized in scienti?c sections of OR 2007.
Operations Research Proceedings 2006 ; Selected Papers of the Annual International Conference of the German Operations Research Society (GOR), Jointly Organized with the Austrian Society of Operations Research (ÖGOR) and the Swiss Society of Operations Research (SVOR)
Contains a selection of papers referring to lectures presented at the symposium ”OperationsResearch 2006” (OR 2006) held at the university of Karlsruhe, September 6 - 8, 2006. This international conference took place under the auspices of the Operations Research Societies of Germany (GOR), ¨ Austria (OGOR), and Switzerland (SVOR). The symposiumwas attended by morethan 600academicsand practiti- ers from 35 countries. It presented the state of the art in Operations Research and related areas in Economics, Mathematics, and Computer Science and demonstrated the broad applicability of its core themes, placing particular emphasis on Basel II, one of the most topical challenges of Operations - search. The scienti?c program consisted of two plenary talks, eleven semi-plenary talks and more than 400 contributed papers, selected by the program c- mittee and arranged in 19 sections.
Operations research proceedings 2005 ; Selected papers of the Annual International Conference of the German Operations Research Society (GOR)
It attracted academics and practitioners working in various fields of Operations Research and provided them with the most recent advances in Operations Research as well as related areas in Economics, Mathematics, and Computer Science including the special interest streams Logistics and New Maritime Businesses.
Operations Research Proceedings 2004 ; Selected Papers of the Annual International Conference of the German Operations Research Society (GOR) - Jointly Organized with the Netherlands Society for Operations Research (NGB), Tilburg, September 1-3, 2004
Contains a selection of papers referring to lectures presented at the symposium "Operations Research 2004" (OR 2004) held at Tilburg University, September 1-3, 2004. This international conference took place under the auspices of the German Operations Research Society (GOR) and the Dutch Operations Research Society (NGB). The symposium had about 500 participants from more than 30 countries all over the world. It attracted academicians and practitioners working in various fields of Operations Research and provided them with the most recent ad vances in Operations Research and related areas in Economics, Mathematics, and Computer Science. The program consisted of 4 plenary and 19 semi-plenary talks and more than 300 contributed presentations, selected by the program committee, to be presented in 20 sections. Due to a limited number of pages available for the proceedings volume, the length of each article as well as the total number of accepted contributions had to be restricted. Submitted manuscripts have therefore been reviewed and 59 of them have been selected for publication
Operational Semantics for Timed Systems : A Non-standard Approach to Uniform Modeling of Timed and Hybrid Systems
Dedicated to a novel approach for uniform modeling of timed and hybrid systems. The author introduces a time model that allows for both the description of discrete time steps and continuous processes with a discrete time model with infinitesimal step widths.The underlying mathematical structure of this time model is based on the concepts of non-standard analysis. The discrete modeling, i.e., the description of sequential discrete algorithms at different abstraction levels, is done using the abstract state machines formalism. The presentation is well balanced between theoretical elaboration and critical discussion of the applicability of the theoretical results by means of appropriate case studies. The new temporal semantics proposed helps theoreticians as well as practitioners in gaining a better understanding of time models and in building better ...
Open Quantum Systems III : Recent Developments
Present in a self-contained way the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications. Volume III is devoted to recent developments and applications. The topics discussed include the non-equilibrium properties of open quantum systems, the Fermi Golden Rule and weak coupling limit, quantum irreversibility and decoherence, qualitative behaviour of quantum Markov semigroups and continual quantum measurements.
Open Quantum Systems II : The Markovian Approach
These books present in a self-contained way the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications. Volume II is dedicated to the Markovian formalism of classical and quantum open systems. A complete exposition of noise theory, Markov processes and stochastic differential equations, both in the classical and the quantum context, is provided. These mathematical tools are put into perspective with physical motivations and applications.
Open Quantum Systems I : The Hamiltonian Approach
These books present in a self-contained way the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications. This Volume, I the Hamiltonian description of quantum open systems is discussed. This includes an introduction to quantum statistical mechanics and its operator algebraic formulation, modular theory, spectral analysis and their applications to quantum dynamical systems.
