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Partial Differential Equations In Economics And Finance
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Book Synopsis Partial Differential Equations in Economics and Finance by : Suren Basov
Download or read book Partial Differential Equations in Economics and Finance written by Suren Basov and published by Nova Publishers. This book was released on 2007 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews the basic theory of partial differential equations of the first and second order and discusses their applications in economics and finance. It starts with well-known applications to consumer and producer theory, and to the theory of option pricing and then introduces new applications that emerge from current research (some of which is the author's own) in bounded rationality, game theory, and multi-dimensional screening.
Book Synopsis Numerical Partial Differential Equations in Finance Explained by : Karel in 't Hout
Download or read book Numerical Partial Differential Equations in Finance Explained written by Karel in 't Hout and published by Springer. This book was released on 2017-09-02 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a first, basic introduction into the valuation of financial options via the numerical solution of partial differential equations (PDEs). It provides readers with an easily accessible text explaining main concepts, models, methods and results that arise in this approach. In keeping with the series style, emphasis is placed on intuition as opposed to full rigor, and a relatively basic understanding of mathematics is sufficient. The book provides a wealth of examples, and ample numerical experiments are givento illustrate the theory. The main focus is on one-dimensional financial PDEs, notably the Black-Scholes equation. The book concludes with a detailed discussion of the important step towards two-dimensional PDEs in finance.
Book Synopsis Numerical Methods in Computational Finance by : Daniel J. Duffy
Download or read book Numerical Methods in Computational Finance written by Daniel J. Duffy and published by John Wiley & Sons. This book was released on 2022-03-14 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a detailed and step-by-step introduction to the mathematical foundations of ordinary and partial differential equations, their approximation by the finite difference method and applications to computational finance. The book is structured so that it can be read by beginners, novices and expert users. Part A Mathematical Foundation for One-Factor Problems Chapters 1 to 7 introduce the mathematical and numerical analysis concepts that are needed to understand the finite difference method and its application to computational finance. Part B Mathematical Foundation for Two-Factor Problems Chapters 8 to 13 discuss a number of rigorous mathematical techniques relating to elliptic and parabolic partial differential equations in two space variables. In particular, we develop strategies to preprocess and modify a PDE before we approximate it by the finite difference method, thus avoiding ad-hoc and heuristic tricks. Part C The Foundations of the Finite Difference Method (FDM) Chapters 14 to 17 introduce the mathematical background to the finite difference method for initial boundary value problems for parabolic PDEs. It encapsulates all the background information to construct stable and accurate finite difference schemes. Part D Advanced Finite Difference Schemes for Two-Factor Problems Chapters 18 to 22 introduce a number of modern finite difference methods to approximate the solution of two factor partial differential equations. This is the only book we know of that discusses these methods in any detail. Part E Test Cases in Computational Finance Chapters 23 to 26 are concerned with applications based on previous chapters. We discuss finite difference schemes for a wide range of one-factor and two-factor problems. This book is suitable as an entry-level introduction as well as a detailed treatment of modern methods as used by industry quants and MSc/MFE students in finance. The topics have applications to numerical analysis, science and engineering. More on computational finance and the author’s online courses, see www.datasim.nl.
Book Synopsis Applications of Stochastic Calculus and Partial Differential Equations in Financial Economics by : Tiberiu Florin Tomita
Download or read book Applications of Stochastic Calculus and Partial Differential Equations in Financial Economics written by Tiberiu Florin Tomita and published by . This book was released on 2003 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Difference Methods in Financial Engineering by : Daniel J. Duffy
Download or read book Finite Difference Methods in Financial Engineering written by Daniel J. Duffy and published by John Wiley & Sons. This book was released on 2013-10-28 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: The world of quantitative finance (QF) is one of the fastest growing areas of research and its practical applications to derivatives pricing problem. Since the discovery of the famous Black-Scholes equation in the 1970's we have seen a surge in the number of models for a wide range of products such as plain and exotic options, interest rate derivatives, real options and many others. Gone are the days when it was possible to price these derivatives analytically. For most problems we must resort to some kind of approximate method. In this book we employ partial differential equations (PDE) to describe a range of one-factor and multi-factor derivatives products such as plain European and American options, multi-asset options, Asian options, interest rate options and real options. PDE techniques allow us to create a framework for modeling complex and interesting derivatives products. Having defined the PDE problem we then approximate it using the Finite Difference Method (FDM). This method has been used for many application areas such as fluid dynamics, heat transfer, semiconductor simulation and astrophysics, to name just a few. In this book we apply the same techniques to pricing real-life derivative products. We use both traditional (or well-known) methods as well as a number of advanced schemes that are making their way into the QF literature: Crank-Nicolson, exponentially fitted and higher-order schemes for one-factor and multi-factor options Early exercise features and approximation using front-fixing, penalty and variational methods Modelling stochastic volatility models using Splitting methods Critique of ADI and Crank-Nicolson schemes; when they work and when they don't work Modelling jumps using Partial Integro Differential Equations (PIDE) Free and moving boundary value problems in QF Included with the book is a CD containing information on how to set up FDM algorithms, how to map these algorithms to C++ as well as several working programs for one-factor and two-factor models. We also provide source code so that you can customize the applications to suit your own needs.
Book Synopsis The Economics of Continuous-Time Finance by : Bernard Dumas
Download or read book The Economics of Continuous-Time Finance written by Bernard Dumas and published by MIT Press. This book was released on 2017-10-27 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to economic applications of the theory of continuous-time finance that strikes a balance between mathematical rigor and economic interpretation of financial market regularities. This book introduces the economic applications of the theory of continuous-time finance, with the goal of enabling the construction of realistic models, particularly those involving incomplete markets. Indeed, most recent applications of continuous-time finance aim to capture the imperfections and dysfunctions of financial markets—characteristics that became especially apparent during the market turmoil that started in 2008. The book begins by using discrete time to illustrate the basic mechanisms and introduce such notions as completeness, redundant pricing, and no arbitrage. It develops the continuous-time analog of those mechanisms and introduces the powerful tools of stochastic calculus. Going beyond other textbooks, the book then focuses on the study of markets in which some form of incompleteness, volatility, heterogeneity, friction, or behavioral subtlety arises. After presenting solutions methods for control problems and related partial differential equations, the text examines portfolio optimization and equilibrium in incomplete markets, interest rate and fixed-income modeling, and stochastic volatility. Finally, it presents models where investors form different beliefs or suffer frictions, form habits, or have recursive utilities, studying the effects not only on optimal portfolio choices but also on equilibrium, or the price of primitive securities. The book strikes a balance between mathematical rigor and the need for economic interpretation of financial market regularities, although with an emphasis on the latter.
Book Synopsis Mathematics for Economics and Finance by : Martin Anthony
Download or read book Mathematics for Economics and Finance written by Martin Anthony and published by Cambridge University Press. This book was released on 1996-07-13 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics has become indispensable in the modelling of economics, finance, business and management. Without expecting any particular background of the reader, this book covers the following mathematical topics, with frequent reference to applications in economics and finance: functions, graphs and equations, recurrences (difference equations), differentiation, exponentials and logarithms, optimisation, partial differentiation, optimisation in several variables, vectors and matrices, linear equations, Lagrange multipliers, integration, first-order and second-order differential equations. The stress is on the relation of maths to economics, and this is illustrated with copious examples and exercises to foster depth of understanding. Each chapter has three parts: the main text, a section of further worked examples and a summary of the chapter together with a selection of problems for the reader to attempt. For students of economics, mathematics, or both, this book provides an introduction to mathematical methods in economics and finance that will be welcomed for its clarity and breadth.
Book Synopsis Numerical Methods in Finance and Economics by : Paolo Brandimarte
Download or read book Numerical Methods in Finance and Economics written by Paolo Brandimarte and published by John Wiley & Sons. This book was released on 2013-06-06 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stochastic Calculus and Differential Equations for Physics and Finance by : Joseph L. McCauley
Download or read book Stochastic Calculus and Differential Equations for Physics and Finance written by Joseph L. McCauley and published by Cambridge University Press. This book was released on 2013-02-21 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides graduate students and practitioners in physics and economics with a better understanding of stochastic processes.
Book Synopsis Estimation of Partial Differential Equations with Applications to Finance by : Dennis Kristensen
Download or read book Estimation of Partial Differential Equations with Applications to Finance written by Dennis Kristensen and published by . This book was released on 2004 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematical Modeling in Economics and Finance: Probability, Stochastic Processes, and Differential Equations by : Steven R. Dunbar
Download or read book Mathematical Modeling in Economics and Finance: Probability, Stochastic Processes, and Differential Equations written by Steven R. Dunbar and published by American Mathematical Soc.. This book was released on 2019-04-03 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Modeling in Economics and Finance is designed as a textbook for an upper-division course on modeling in the economic sciences. The emphasis throughout is on the modeling process including post-modeling analysis and criticism. It is a textbook on modeling that happens to focus on financial instruments for the management of economic risk. The book combines a study of mathematical modeling with exposure to the tools of probability theory, difference and differential equations, numerical simulation, data analysis, and mathematical analysis. Students taking a course from Mathematical Modeling in Economics and Finance will come to understand some basic stochastic processes and the solutions to stochastic differential equations. They will understand how to use those tools to model the management of financial risk. They will gain a deep appreciation for the modeling process and learn methods of testing and evaluation driven by data. The reader of this book will be successfully positioned for an entry-level position in the financial services industry or for beginning graduate study in finance, economics, or actuarial science. The exposition in Mathematical Modeling in Economics and Finance is crystal clear and very student-friendly. The many exercises are extremely well designed. Steven Dunbar is Professor Emeritus of Mathematics at the University of Nebraska and he has won both university-wide and MAA prizes for extraordinary teaching. Dunbar served as Director of the MAA's American Mathematics Competitions from 2004 until 2015. His ability to communicate mathematics is on full display in this approachable, innovative text.
Book Synopsis Elements of Mathematics for Economics and Finance by : Vassilis C. Mavron
Download or read book Elements of Mathematics for Economics and Finance written by Vassilis C. Mavron and published by Springer Science & Business Media. This book was released on 2007-03-06 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book equips undergraduates with the mathematical skills required for degree courses in economics, finance, management, and business studies. The fundamental ideas are described in the simplest mathematical terms, highlighting threads of common mathematical theory in the various topics. Coverage helps readers become confident and competent in the use of mathematical tools and techniques that can be applied to a range of problems.
Author :Emanuela Rosazza Gianin Publisher :Springer Science & Business Media ISBN 13 :3319013572 Total Pages :286 pages Book Rating :4.3/5 (19 download)
Book Synopsis Mathematical Finance: Theory Review and Exercises by : Emanuela Rosazza Gianin
Download or read book Mathematical Finance: Theory Review and Exercises written by Emanuela Rosazza Gianin and published by Springer Science & Business Media. This book was released on 2014-02-10 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book collects over 120 exercises on different subjects of Mathematical Finance, including Option Pricing, Risk Theory, and Interest Rate Models. Many of the exercises are solved, while others are only proposed. Every chapter contains an introductory section illustrating the main theoretical results necessary to solve the exercises. The book is intended as an exercise textbook to accompany graduate courses in mathematical finance offered at many universities as part of degree programs in Applied and Industrial Mathematics, Mathematical Engineering, and Quantitative Finance.
Book Synopsis The Mathematics of Financial Derivatives by : Paul Wilmott
Download or read book The Mathematics of Financial Derivatives written by Paul Wilmott and published by Cambridge University Press. This book was released on 1995-09-29 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic option theory - Numerical methods - Further option theory - Interest rate derivative products.
Book Synopsis An Introduction to Wavelets and Other Filtering Methods in Finance and Economics by : Ramazan Gençay
Download or read book An Introduction to Wavelets and Other Filtering Methods in Finance and Economics written by Ramazan Gençay and published by Elsevier. This book was released on 2001-10-12 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Wavelets and Other Filtering Methods in Finance and Economics presents a unified view of filtering techniques with a special focus on wavelet analysis in finance and economics. It emphasizes the methods and explanations of the theory that underlies them. It also concentrates on exactly what wavelet analysis (and filtering methods in general) can reveal about a time series. It offers testing issues which can be performed with wavelets in conjunction with the multi-resolution analysis. The descriptive focus of the book avoids proofs and provides easy access to a wide spectrum of parametric and nonparametric filtering methods. Examples and empirical applications will show readers the capabilities, advantages, and disadvantages of each method. The first book to present a unified view of filtering techniques Concentrates on exactly what wavelets analysis and filtering methods in general can reveal about a time series Provides easy access to a wide spectrum of parametric and non-parametric filtering methods
Book Synopsis Introduction to the Theory of Linear Partial Differential Equations by : J. Chazarain
Download or read book Introduction to the Theory of Linear Partial Differential Equations written by J. Chazarain and published by Elsevier. This book was released on 2011-08-18 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to the Theory of Linear Partial Differential Equations
Book Synopsis Partial Differential Equations by : Wolfgang Arendt
Download or read book Partial Differential Equations written by Wolfgang Arendt and published by Springer Nature. This book was released on 2023-01-01 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach. A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses on finite difference and finite element methods. Computer-aided calculation with MapleTM completes the book. Throughout, three fundamental examples are studied with different tools: Poisson’s equation, the heat equation, and the wave equation on Euclidean domains. The Black–Scholes equation from mathematical finance is one of several opportunities for extension. Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upper-undergraduate level are assumed.
