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.
1 Motivation 3
2 Financial theory 23
3 Basics of numerical analysis 137
4 Numerical integration : deterministic and Monte Carlo methods 209
5 Finite difference methods for partial differential equations 289
6 Convex optimization 327
7 Option pricing by binomial and trinomial lattices 401
8 Option pricing by Monte Carlo methods 429
9 Option pricing by finite difference methods 475
10 Dynamic programming 495
11 Linear stochastic programming models with recourse 525
12 Non-convex optimization 563
App. A Introduction to MATLAB programming 603
App. B Refresher on probability theory and statistics 623
App. C Introduction to AMPL 647
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