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.

A state-of-the-art introduction to the powerful mathematical andstatistical tools used in the field of financeThe use of mathematical models and numerical techniques is apractice employed by a growing number of applied mathematiciansworking on applications in finance. Reflecting this developmentNumerical Methods in Finance and Economics: A MATLAB?-BasedIntroduction, Second Edition bridges the gap between financialtheory and computational practice while showing readers how toutilize MATLAB?--the powerful numerical computing environment--forfinancial applications.The author provides an essential foundation in finance andnumerical analysis in addition to background material for studentsfrom both engineering and economics perspectives. A wide range oftopics is covered, including standard numerical analysis methodsMonte Carlo methods to simulate systems affected by significantuncertainty, and optimization methods to find an optimal set ofdecisions.Among this book's most outstanding features is the integration ofMATLAB?, which helps students and practitioners solve relevantproblems in finance, such as portfolio management and derivativespricing. This tutorial is useful in connecting theory with practicein the application of classical numerical methods and advancedmethods, while illustrating underlying algorithmic concepts inconcrete terms.Newly featured in the Second Edition:* In-depth treatment of Monte Carlo methods with due attention paidto variance reduction strategies* New appendix on AMPL in order to better illustrate theoptimization models in Chapters 11 and 12* New chapter on binomial and trinomial lattices* Additional treatment of partial differential equations with twospace dimensions* Expanded treatment within the chapter on financial theory toprovide a more thorough background for engineers not familiar withfinance* New coverage of advanced optimization methods and applicationslater in the textNumerical Methods in Finance and Economics: A MATLAB?-BasedIntroduction, Second Edition presents basic treatments and morespecialized literature, and it also uses algebraic languages, suchas AMPL, to connect the pencil-and-paper statement of anoptimization model with its solution by a software library.Offering computational practice in both financial engineering andeconomics fields, this book equips practitioners with the necessarytechniques to measure and manage risk.

Preface to the Second Edition.From the Preface to the First Edition.PART I. BACKGROUND.1. Motivation.2. Financial Theory.PART II. NUMERICAL METHODS.3. Basics of Numerical Analysis.4. Numerical Integration: Deterministic and Monte CarloMethods.5. Finite Difference Methods for Partial DifferentialEquations.6. Convex Optimization.PART III. PRICING EQUITY OPTIONS.7. Option Pricing by Binomial and Trinomial Lattices.8. Option Pricing by Monte Carlo Methods.9. Option Pricing by Finite Difference Methods.PART IV. ADVANCED OPTMIZATION MODELS AND METHODS.10. Dynamic Programming.11. Linear Stochastic Programming Models with Recourse.12. Non-Convex Optimization.PART V. APPENDICES.Appendix A. Introduction to MATLAB Programming.Appendix B. Refresher on Probability theory and Statistics.Appendix C. Introduction to AMPL.Index.