Numerical Methods and Optimization in Finance

Author: Manfred Gilli,Dietmar Maringer,Enrico Schumann

Publisher: Academic Press

ISBN: 0123756626

Category: Business & Economics

Page: 584

View: 2057

This book describes computational finance tools. It covers fundamental numerical analysis and computational techniques, such as option pricing, and gives special attention to simulation and optimization. Many chapters are organized as case studies around portfolio insurance and risk estimation problems. In particular, several chapters explain optimization heuristics and how to use them for portfolio selection and in calibration of estimation and option pricing models. Such practical examples allow readers to learn the steps for solving specific problems and apply these steps to others. At the same time, the applications are relevant enough to make the book a useful reference. Matlab and R sample code is provided in the text and can be downloaded from the book's website. Shows ways to build and implement tools that help test ideas Focuses on the application of heuristics; standard methods receive limited attention Presents as separate chapters problems from portfolio optimization, estimation of econometric models, and calibration of option pricing models

Numerical Methods in Finance and Economics

A MATLAB-Based Introduction

Author: Paolo Brandimarte

Publisher: John Wiley & Sons

ISBN: 1118625579

Category: Mathematics

Page: 696

View: 8098

A state-of-the-art introduction to the powerful mathematical and statistical tools used in the field of finance The use of mathematical models and numerical techniques is a practice employed by a growing number of applied mathematicians working on applications in finance. Reflecting this development, Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition bridges the gap between financial theory and computational practice while showing readers how to utilize MATLAB?--the powerful numerical computing environment--for financial applications. The author provides an essential foundation in finance and numerical analysis in addition to background material for students from both engineering and economics perspectives. A wide range of topics is covered, including standard numerical analysis methods, Monte Carlo methods to simulate systems affected by significant uncertainty, and optimization methods to find an optimal set of decisions. Among this book's most outstanding features is the integration of MATLAB?, which helps students and practitioners solve relevant problems in finance, such as portfolio management and derivatives pricing. This tutorial is useful in connecting theory with practice in the application of classical numerical methods and advanced methods, while illustrating underlying algorithmic concepts in concrete terms. Newly featured in the Second Edition: * In-depth treatment of Monte Carlo methods with due attention paid to variance reduction strategies * New appendix on AMPL in order to better illustrate the optimization models in Chapters 11 and 12 * New chapter on binomial and trinomial lattices * Additional treatment of partial differential equations with two space dimensions * Expanded treatment within the chapter on financial theory to provide a more thorough background for engineers not familiar with finance * New coverage of advanced optimization methods and applications later in the text Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition presents basic treatments and more specialized literature, and it also uses algebraic languages, such as AMPL, to connect the pencil-and-paper statement of an optimization model with its solution by a software library. Offering computational practice in both financial engineering and economics fields, this book equips practitioners with the necessary techniques to measure and manage risk.

Numerical Methods in Finance

A MATLAB-Based Introduction

Author: Paolo Brandimarte

Publisher: John Wiley & Sons

ISBN: 0471461695

Category: Mathematics

Page: 432

View: 9804

Balanced coverage of the methodology and theory of numericalmethods in finance Numerical Methods in Finance bridges the gap between financialtheory and computational practice while helping students andpractitioners exploit MATLAB for financial applications. Paolo Brandimarte covers the basics of finance and numericalanalysis and provides background material that suits the needs ofstudents from both financial engineering and economicsperspectives. Classical numerical analysis methods; optimization,including less familiar topics such as stochastic and integerprogramming; simulation, including low discrepancy sequences; andpartial differential equations are covered in detail. Extensiveillustrative examples of the application of all of thesemethodologies are also provided. The text is primarily focused on MATLAB-based application, but alsoincludes descriptions of other readily available toolboxes that arerelevant to finance. Helpful appendices on the basics of MATLAB andprobability theory round out this balanced coverage. Accessible forstudents-yet still a useful reference for practitioners-NumericalMethods in Finance offers an expert introduction to powerful toolsin finance.

Numerical Methods in Finance

Author: L. C. G. Rogers,D. Talay

Publisher: Cambridge University Press

ISBN: 9780521573542

Category: Business & Economics

Page: 326

View: 4850

Numerical Methods in Finance describes a wide variety of numerical methods used in financial analysis.

Implementing Models in Quantitative Finance: Methods and Cases

Author: Gianluca Fusai,Andrea Roncoroni

Publisher: Springer Science & Business Media

ISBN: 9783540499596

Category: Business & Economics

Page: 607

View: 2690

This book puts numerical methods in action for the purpose of solving practical problems in quantitative finance. The first part develops a toolkit in numerical methods for finance. The second part proposes twenty self-contained cases covering model simulation, asset pricing and hedging, risk management, statistical estimation and model calibration. Each case develops a detailed solution to a concrete problem arising in applied financial management and guides the user towards a computer implementation. The appendices contain "crash courses" in VBA and Matlab programming languages.

Numerical Methods in Economics

Author: Kenneth L. Judd,Kenneth L.. Judd

Publisher: MIT Press

ISBN: 9780262100717

Category: Business & Economics

Page: 633

View: 6256

"Judd's book is a masterpiece which will help transform the way economic theory is done. It harnesses the computer revolution in the service of economic theory by collecting together a whole array of numerical methods to simulate and quantify models that used to be purely algebraic and qualitative." -- Avinash K. Dixit, Sherrerd University Professor of Economics, Princeton University To harness the full power of computer technology, economists need to use a broad range of mathematical techniques. In this book, Kenneth Judd presents techniques from the numerical analysis and applied mathematics literatures and shows how to use them in economic analyses. The book is divided into five parts. Part I provides a general introduction. Part II presents basics from numerical analysis on "Rn," including linear equations, iterative methods, optimization, nonlinear equations, approximation methods, numerical integration and differentiation, and Monte Carlo methods. Part III covers methods for dynamic problems, including finite difference methods, projection methods, and numerical dynamic programming. Part IV covers perturbation and asymptotic solution methods. Finally, Part V covers applications to dynamic equilibrium analysis, including solution methods for perfect foresight models and rational expectation models. A web site contains supplementary material including programs and answers to exercises.

Numerical Methods and Optimization

An Introduction

Author: Sergiy Butenko,Panos M. Pardalos

Publisher: CRC Press

ISBN: 1466577789

Category: Business & Economics

Page: 412

View: 3890

For students in industrial and systems engineering (ISE) and operations research (OR) to understand optimization at an advanced level, they must first grasp the analysis of algorithms, computational complexity, and other concepts and modern developments in numerical methods. Satisfying this prerequisite, Numerical Methods and Optimization: An Introduction combines the materials from introductory numerical methods and introductory optimization courses into a single text. This classroom-tested approach enriches a standard numerical methods syllabus with optional chapters on numerical optimization and provides a valuable numerical methods background for students taking an introductory OR or optimization course. The first part of the text introduces the necessary mathematical background, the digital representation of numbers, and different types of errors associated with numerical methods. The second part explains how to solve typical problems using numerical methods. Focusing on optimization methods, the final part presents basic theory and algorithms for linear and nonlinear optimization. The book assumes minimal prior knowledge of the topics. Taking a rigorous yet accessible approach to the material, it includes some mathematical proofs as samples of rigorous analysis but in most cases, uses only examples to illustrate the concepts. While the authors provide a MATLAB® guide and code available for download, the book can be used with other software packages.

A Workout in Computational Finance

Author: Andreas Binder,Michael Aichinger

Publisher: John Wiley & Sons

ISBN: 111997349X

Category: Business & Economics

Page: 336

View: 1844

A comprehensive introduction to various numerical methods used in computational finance today Quantitative skills are a prerequisite for anyone working in finance or beginning a career in the field, as well as risk managers. A thorough grounding in numerical methods is necessary, as is the ability to assess their quality, advantages, and limitations. This book offers a thorough introduction to each method, revealing the numerical traps that practitioners frequently fall into. Each method is referenced with practical, real-world examples in the areas of valuation, risk analysis, and calibration of specific financial instruments and models. It features a strong emphasis on robust schemes for the numerical treatment of problems within computational finance. Methods covered include PDE/PIDE using finite differences or finite elements, fast and stable solvers for sparse grid systems, stabilization and regularization techniques for inverse problems resulting from the calibration of financial models to market data, Monte Carlo and Quasi Monte Carlo techniques for simulating high dimensional systems, and local and global optimization tools to solve the minimization problem.

Handbook of Computational and Numerical Methods in Finance

Author: Svetlozar T. Rachev

Publisher: Springer Science & Business Media

ISBN: 9780817632199

Category: Business & Economics

Page: 435

View: 338

Numerical Methods in Finance have recently emerged as a new discipline at the intersection of probability theory, finance and numerical analysis. They bridge the gap between financial theory and computational practice and provide solutions to problems where analytical methods are often non-applicable. Numerical methods are more and more used in several topics of financial analy sis: computation of complex derivatives; market, credit and operational risk assess ment, asset liability management, optimal portfolio theory, financial econometrics and others. Although numerical methods in finance have been studied intensively in recent years, many theoretical and practical financial aspects have yet to be explored. This volume presents current research focusing on various numerical methods in finance. The contributions cover methodological issues. Genetic Algorithms, Neural Net works, Monte-Carlo methods, Finite Difference Methods, Stochastic Portfolio Opti mization as well as the application of other numerical methods in finance and risk management. As editor, I am grateful to the contributors for their fruitful collaboration. I would particularly like to thankStefan Trueck and Carlo Marinelli for the excellent editorial assistance received over the progress of this project. Thomas Plum did a splendid word-processingjob in preparing the manuscript. lowe much to George Anastassiou (ConsultantEditor, Birkhauser) and Ann Kostant Executive Editor, Mathematics and Physics, Birkhauser for their help and encouragement.

Applied Computational Economics and Finance

Author: Mario J. Miranda,Paul L. Fackler

Publisher: MIT Press

ISBN: 0262291754

Category: Business & Economics

Page: 528

View: 9432

This book presents a variety of computational methods used to solve dynamic problems in economics and finance. It emphasizes practical numerical methods rather than mathematical proofs and focuses on techniques that apply directly to economic analyses. The examples are drawn from a wide range of subspecialties of economics and finance, with particular emphasis on problems in agricultural and resource economics, macroeconomics, and finance. The book also provides an extensive Web-site library of computer utilities and demonstration programs.The book is divided into two parts. The first part develops basic numerical methods, including linear and nonlinear equation methods, complementarity methods, finite-dimensional optimization, numerical integration and differentiation, and function approximation. The second part presents methods for solving dynamic stochastic models in economics and finance, including dynamic programming, rational expectations, and arbitrage pricing models in discrete and continuous time. The book uses MATLAB to illustrate the algorithms and includes a utilities toolbox to help readers develop their own computational economics applications.

Numerical Methods in Engineering with Python

Author: Jaan Kiusalaas

Publisher: Cambridge University Press

ISBN: 113948415X

Category: Technology & Engineering

Page: 422

View: 7109

This text is for engineering students and a reference for practising engineers, especially those who wish to explore Python. This new edition features 18 additional exercises and the addition of rational function interpolation. Brent's method of root finding was replaced by Ridder's method, and the Fletcher-Reeves method of optimization was dropped in favor of the downhill simplex method. Each numerical method is explained in detail, and its shortcomings are pointed out. The examples that follow individual topics fall into two categories: hand computations that illustrate the inner workings of the method and small programs that show how the computer code is utilized in solving a problem. This second edition also includes more robust computer code with each method, which is available on the book website. This code is made simple and easy to understand by avoiding complex bookkeeping schemes, while maintaining the essential features of the method.

Stochastic Optimization Methods in Finance and Energy

New Financial Products and Energy Market Strategies

Author: Marida Bertocchi,Giorgio Consigli,Michael A. H. Dempster

Publisher: Springer Science & Business Media

ISBN: 9781441995865

Category: Business & Economics

Page: 476

View: 9368

This volume presents a collection of contributions dedicated to applied problems in the financial and energy sectors that have been formulated and solved in a stochastic optimization framework. The invited authors represent a group of scientists and practitioners, who cooperated in recent years to facilitate the growing penetration of stochastic programming techniques in real-world applications, inducing a significant advance over a large spectrum of complex decision problems. After the recent widespread liberalization of the energy sector in Europe and the unprecedented growth of energy prices in international commodity markets, we have witnessed a significant convergence of strategic decision problems in the energy and financial sectors. This has often resulted in common open issues and has induced a remarkable effort by the industrial and scientific communities to facilitate the adoption of advanced analytical and decision tools. The main concerns of the financial community over the last decade have suddenly penetrated the energy sector inducing a remarkable scientific and practical effort to address previously unforeseeable management problems. Stochastic Optimization Methods in Finance and Energy: New Financial Products and Energy Markets Strategies aims to include in a unified framework for the first time an extensive set of contributions related to real-world applied problems in finance and energy, leading to a common methodological approach and in many cases having similar underlying economic and financial implications. Part 1 of the book presents 6 chapters related to financial applications; Part 2 presents 7 chapters on energy applications; and Part 3 presents 5 chapters devoted to specific theoretical and computational issues.

Classical and Modern Numerical Analysis

Theory, Methods and Practice

Author: Azmy S. Ackleh,Edward James Allen,R. Baker Kearfott,Padmanabhan Seshaiyer

Publisher: CRC Press

ISBN: 9781420091588

Category: Mathematics

Page: 628

View: 3803

Classical and Modern Numerical Analysis: Theory, Methods and Practice provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical linear algebra, and optimization. It prepares graduate students for taking doctoral examinations in numerical analysis. The text covers the main areas of introductory numerical analysis, including the solution of nonlinear equations, numerical linear algebra, ordinary differential equations, approximation theory, numerical integration, and boundary value problems. Focusing on interval computing in numerical analysis, it explains interval arithmetic, interval computation, and interval algorithms. The authors illustrate the concepts with many examples as well as analytical and computational exercises at the end of each chapter. This advanced, graduate-level introduction to the theory and methods of numerical analysis supplies the necessary background in numerical methods so that students can apply the techniques and understand the mathematical literature in this area. Although the book is independent of a specific computer program, MATLAB® code is available on the authors' website to illustrate various concepts.

Geometric Methods and Optimization Problems

Author: Vladimir Boltyanski,Horst Martini,V. Soltan,Valeriĭ Petrovich Soltan

Publisher: Springer Science & Business Media

ISBN: 9780792354543

Category: Computers

Page: 429

View: 6891

This book focuses on three disciplines of applied mathematics: control theory, location science and computational geometry. The authors show how methods and tools from convex geometry in a wider sense can help solve various problems from these disciplines. More precisely they consider mainly the tent method (as an application of a generalized separation theory of convex cones) in nonclassical variational calculus, various median problems in Euclidean and other Minkowski spaces (including a detailed discussion of the Fermat-Torricelli problem) and different types of partitionings of topologically complicated polygonal domains into a minimum number of convex pieces. Figures are used extensively throughout the book and there is also a large collection of exercises. Audience: Graduate students, teachers and researchers.

Numerical Optimization

Author: Jorge Nocedal,Stephen Wright

Publisher: Springer Science & Business Media

ISBN: 0387227423

Category: Mathematics

Page: 636

View: 2866

The new edition of this book presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on methods best suited to practical problems. This edition has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are widely used in practice and are the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience.