Numerical Methods and Optimization in Finance

Author: Manfred Gilli,Dietmar Maringer,Enrico Schumann

Publisher: Academic Press

ISBN: 0123756626

Category: Business & Economics

Page: 584

View: 735

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: 7861

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: 3863

Balanced coverage of the methodology and theory of numerical methods in finance Numerical Methods in Finance bridges the gap between financial theory and computational practice while helping students and practitioners exploit MATLAB for financial applications. Paolo Brandimarte covers the basics of finance and numerical analysis and provides background material that suits the needs of students from both financial engineering and economics perspectives. Classical numerical analysis methods; optimization, including less familiar topics such as stochastic and integer programming; simulation, including low discrepancy sequences; and partial differential equations are covered in detail. Extensive illustrative examples of the application of all of these methodologies are also provided. The text is primarily focused on MATLAB-based application, but also includes descriptions of other readily available toolboxes that are relevant to finance. Helpful appendices on the basics of MATLAB and probability theory round out this balanced coverage. Accessible for students-yet still a useful reference for practitioners-Numerical Methods in Finance offers an expert introduction to powerful tools in finance.

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: 3890

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.

Optionsbewertung und Portfolio-Optimierung

Moderne Methoden der Finanzmathematik

Author: Ralf Korn,Elke Korn

Publisher: Springer-Verlag

ISBN: 3322832104

Category: Business & Economics

Page: 294

View: 3716

Es werden die typischen Aufgabenstellungen der zeitstetigen Modellierung von Finanzmärkten wie Optionsbewertung (insbesondere auch die Black-Scholes-Formel und zugehörige Varianten) und Portfolio-Optimierung (Bestimmen optimaler Investmentstrategien) behandelt. Die benötigten mathematischen Werkzeuge (wie z. B. Brownsche Bewegung, Martingaltheorie, Ito-Kalkül, stochastische Steuerung) werden in selbständigen Exkursen bereitgestellt. Das Buch eignet sich als Grundlage einer Vorlesung, die sich an einen Grundkurs in Stochastik anschließt. Es richtet sich an Mathematiker, Finanz- und Wirtschaftsmathematiker in Studium und Beruf und ist aufgrund seiner modularen Struktur auch für Praktiker in den Bereichen Banken und Versicherungen geeignet.

Numerical Methods and Optimization

An Introduction

Author: Sergiy Butenko,Panos M. Pardalos

Publisher: CRC Press

ISBN: 1466577789

Category: Business & Economics

Page: 412

View: 4246

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.

Numerical Methods in Economics

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

Publisher: MIT Press

ISBN: 9780262100717

Category: Business & Economics

Page: 633

View: 5977

"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.

Applied Computational Economics and Finance

Author: Mario J. Miranda,Paul L. Fackler

Publisher: MIT Press

ISBN: 0262291754

Category: Business & Economics

Page: 528

View: 2037

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.

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: 3493

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.

A Workout in Computational Finance

Author: Andreas Binder,Michael Aichinger

Publisher: John Wiley & Sons

ISBN: 111997349X

Category: Business & Economics

Page: 336

View: 5498

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.

Computational Methods in Decision-Making, Economics and Finance

Author: Erricos John Kontoghiorghes,B. Rustem,S. Siokos

Publisher: Springer Science & Business Media

ISBN: 9781402008399

Category: Business & Economics

Page: 622

View: 8985

Computing has become essential for the modeling, analysis, and optimization of systems. This book is devoted to algorithms, computational analysis, and decision models. The chapters are organized in two parts: optimization models of decisions and models of pricing and equilibria. Optimization is at the core of rational decision making. Even when the decision maker has more than one goal or there is significant uncertainty in the system, optimization provides a rational framework for efficient decisions. The Markowitz mean-variance formulation is a classical example. The first part of the book is on recent developments in optimization decision models for finance and economics. The first four chapters of this part focus directly on multi-stage problems in finance. Chapters 5-8 involve the use of worst-case robust analysis. Chapters 9-11 are devoted to portfolio optimization. The final four chapters are on transportation-inventory with stochastic demand; optimal investment with CRRA utility; hedging financial contracts; and, automatic differentiation for computational finance. The uncertainty associated with prediction and modeling constantly requires the development of improved methods and models. Similarly, as systems strive towards equilibria, the characterization and computation of equilibria assists analysis and prediction. The second part of the book is devoted to recent research in computational tools and models of equilibria, prediction, and pricing. The first three chapters of this part consider hedging issues in finance. Chapters 19-22 consider prediction and modeling methodologies. Chapters 23-26 focus on auctions and equilibria. Volatility models are investigated in chapters 27-28. The final two chapters investigate risk assessment and product pricing. Audience: Researchers working in computational issues related to economics, finance, and management science.

Numerical Methods in Engineering with Python

Author: Jaan Kiusalaas

Publisher: Cambridge University Press

ISBN: 113948415X

Category: Technology & Engineering

Page: 422

View: 7069

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.

Quantitative Methods

An Introduction for Business Management

Author: Paolo Brandimarte

Publisher: John Wiley & Sons

ISBN: 9781118023488

Category: Mathematics

Page: 800

View: 6183

An accessible introduction to the essential quantitative methods for making valuable business decisions Quantitative methods-research techniques used to analyze quantitative data-enable professionals to organize and understand numbers and, in turn, to make good decisions. Quantitative Methods: An Introduction for Business Management presents the application of quantitative mathematical modeling to decision making in a business management context and emphasizes not only the role of data in drawing conclusions, but also the pitfalls of undiscerning reliance of software packages that implement standard statistical procedures. With hands-on applications and explanations that are accessible to readers at various levels, the book successfully outlines the necessary tools to make smart and successful business decisions. Progressing from beginner to more advanced material at an easy-to-follow pace, the author utilizes motivating examples throughout to aid readers interested in decision making and also provides critical remarks, intuitive traps, and counterexamples when appropriate. The book begins with a discussion of motivations and foundations related to the topic, with introductory presentations of concepts from calculus to linear algebra. Next, the core ideas of quantitative methods are presented in chapters that explore introductory topics in probability, descriptive and inferential statistics, linear regression, and a discussion of time series that includes both classical topics and more challenging models. The author also discusses linear programming models and decision making under risk as well as less standard topics in the field such as game theory and Bayesian statistics. Finally, the book concludes with a focus on selected tools from multivariate statistics, including advanced regression models and data reduction methods such as principal component analysis, factor analysis, and cluster analysis. The book promotes the importance of an analytical approach, particularly when dealing with a complex system where multiple individuals are involved and have conflicting incentives. A related website features Microsoft Excel® workbooks and MATLAB® scripts to illustrate concepts as well as additional exercises with solutions. Quantitative Methods is an excellent book for courses on the topic at the graduate level. The book also serves as an authoritative reference and self-study guide for financial and business professionals, as well as readers looking to reinforce their analytical skills.