{"product_id":"mathematical-methods-for-finance-isbn-9781118312636","title":"Mathematical Methods for Finance","description":"\u003cb\u003eThe mathematical and statistical tools needed in the rapidly growing quantitative finance field\u003c\/b\u003e  \u003cp\u003eWith the rapid growth in quantitative finance, practitioners must achieve a high level of proficiency in math and statistics. \u003ci\u003eMathematical Methods and Statistical Tools for Finance\u003c\/i\u003e, part of the Frank J. Fabozzi Series, has been created with this in mind. Designed to provide the tools needed to apply finance theory to real world financial markets, this book offers a wealth of insights and guidance in practical applications.\u003c\/p\u003e \u003cp\u003eIt contains applications that are broader in scope from what is covered in a typical book on mathematical techniques. Most books focus almost exclusively on derivatives pricing, the applications in this book cover not only derivatives and asset pricing but also risk management—including credit risk management—and portfolio management.\u003c\/p\u003e \u003cul\u003e \u003cli\u003eIncludes an overview of the essential math and statistical skills required to succeed in quantitative finance\u003c\/li\u003e \u003cli\u003eOffers the basic mathematical concepts that apply to the field of quantitative finance, from sets and distances to functions and variables\u003c\/li\u003e \u003cli\u003eThe book also includes information on calculus, matrix algebra, differential equations, stochastic integrals, and much more\u003c\/li\u003e \u003cli\u003eWritten by Sergio Focardi, one of the world's leading authors in high-level finance\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eDrawing on the author's perspectives as a practitioner and academic, each chapter of this book offers a solid foundation in the mathematical tools and techniques need to succeed in today's dynamic world of finance.\u003c\/p\u003e  \u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eAbout the Authors xvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 1 Basic Concepts: Sets, Functions, and Variables 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 2\u003c\/p\u003e \u003cp\u003eSets and Set Operations 2\u003c\/p\u003e \u003cp\u003eDistances and Quantities 6\u003c\/p\u003e \u003cp\u003eFunctions 10\u003c\/p\u003e \u003cp\u003eVariables 10\u003c\/p\u003e \u003cp\u003eKey Points 11\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 2 Differential Calculus 13\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 14\u003c\/p\u003e \u003cp\u003eLimits 15\u003c\/p\u003e \u003cp\u003eContinuity 17\u003c\/p\u003e \u003cp\u003eTotal Variation 19\u003c\/p\u003e \u003cp\u003eThe Notion of Differentiation 19\u003c\/p\u003e \u003cp\u003eCommonly Used Rules for Computing Derivatives 21\u003c\/p\u003e \u003cp\u003eHigher-Order Derivatives 26\u003c\/p\u003e \u003cp\u003eTaylor Series Expansion 34\u003c\/p\u003e \u003cp\u003eCalculus in More Than One Variable 40\u003c\/p\u003e \u003cp\u003eKey Points 41\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 3 Integral Calculus 43\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 44\u003c\/p\u003e \u003cp\u003eRiemann Integrals 44\u003c\/p\u003e \u003cp\u003eLebesgue-Stieltjes Integrals 47\u003c\/p\u003e \u003cp\u003eIndefinite and Improper Integrals 48\u003c\/p\u003e \u003cp\u003eThe Fundamental Theorem of Calculus 51\u003c\/p\u003e \u003cp\u003eIntegral Transforms 52\u003c\/p\u003e \u003cp\u003eCalculus in More Than One Variable 57\u003c\/p\u003e \u003cp\u003eKey Points 57\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 4 Matrix Algebra 59\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 60\u003c\/p\u003e \u003cp\u003eVectors and Matrices Defined 61\u003c\/p\u003e \u003cp\u003eSquare Matrices 63\u003c\/p\u003e \u003cp\u003eDeterminants 66\u003c\/p\u003e \u003cp\u003eSystems of Linear Equations 68\u003c\/p\u003e \u003cp\u003eLinear Independence and Rank 69\u003c\/p\u003e \u003cp\u003eHankel Matrix 70\u003c\/p\u003e \u003cp\u003eVector and Matrix Operations 72\u003c\/p\u003e \u003cp\u003eFinance Application 78\u003c\/p\u003e \u003cp\u003eEigenvalues and Eigenvectors 81\u003c\/p\u003e \u003cp\u003eDiagonalization and Similarity 82\u003c\/p\u003e \u003cp\u003eSingular Value Decomposition 83\u003c\/p\u003e \u003cp\u003eKey Points 83\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 5 Probability: Basic Concepts 85\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 86\u003c\/p\u003e \u003cp\u003eRepresenting Uncertainty with Mathematics 87\u003c\/p\u003e \u003cp\u003eProbability in a Nutshell 89\u003c\/p\u003e \u003cp\u003eOutcomes and Events 91\u003c\/p\u003e \u003cp\u003eProbability 92\u003c\/p\u003e \u003cp\u003eMeasure 93\u003c\/p\u003e \u003cp\u003eRandom Variables 93\u003c\/p\u003e \u003cp\u003eIntegrals 94\u003c\/p\u003e \u003cp\u003eDistributions and Distribution Functions 96\u003c\/p\u003e \u003cp\u003eRandom Vectors 97\u003c\/p\u003e \u003cp\u003eStochastic Processes 100\u003c\/p\u003e \u003cp\u003eProbabilistic Representation of Financial Markets 102\u003c\/p\u003e \u003cp\u003eInformation Structures 103\u003c\/p\u003e \u003cp\u003eFiltration 104\u003c\/p\u003e \u003cp\u003eKey Points 106\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 6 Probability: Random Variables and Expectations 107\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 109\u003c\/p\u003e \u003cp\u003eConditional Probability and Conditional Expectation 110\u003c\/p\u003e \u003cp\u003eMoments and Correlation 112\u003c\/p\u003e \u003cp\u003eCopula Functions 114\u003c\/p\u003e \u003cp\u003eSequences of Random Variables 116\u003c\/p\u003e \u003cp\u003eIndependent and Identically Distributed Sequences 117\u003c\/p\u003e \u003cp\u003eSum of Variables 118\u003c\/p\u003e \u003cp\u003eGaussian Variables 120\u003c\/p\u003e \u003cp\u003eAppproximating the Tails of a Probability Distribution: Cornish-Fisher Expansion and Hermite Polynomials 123\u003c\/p\u003e \u003cp\u003eThe Regression Function 129\u003c\/p\u003e \u003cp\u003eFat Tails and Stable Laws 131\u003c\/p\u003e \u003cp\u003eKey Points 144\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 7 Optimization 147\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 148\u003c\/p\u003e \u003cp\u003eMaxima and Minima 149\u003c\/p\u003e \u003cp\u003eLagrange Multipliers 151\u003c\/p\u003e \u003cp\u003eNumerical Algorithms 156\u003c\/p\u003e \u003cp\u003eCalculus of Variations and Optimal Control Theory 161\u003c\/p\u003e \u003cp\u003eStochastic Programming 163\u003c\/p\u003e \u003cp\u003eApplication to Bond Portfolio: Liability-Funding Strategies 164\u003c\/p\u003e \u003cp\u003eKey Points 178\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 8 Difference Equations 181\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 182\u003c\/p\u003e \u003cp\u003eThe Lag Operator L 183\u003c\/p\u003e \u003cp\u003eHomogeneous Difference Equations 183\u003c\/p\u003e \u003cp\u003eRecursive Calculation of Values of Difference Equations 192\u003c\/p\u003e \u003cp\u003eNonhomogeneous Difference Equations 195\u003c\/p\u003e \u003cp\u003eSystems of Linear Difference Equations 201\u003c\/p\u003e \u003cp\u003eSystems of Homogeneous Linear Difference Equations 202\u003c\/p\u003e \u003cp\u003eKey Points 209\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 9 Differential Equations 211\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 212\u003c\/p\u003e \u003cp\u003eDifferential Equations Defined 213\u003c\/p\u003e \u003cp\u003eOrdinary Differential Equations 213\u003c\/p\u003e \u003cp\u003eSystems of Ordinary Differential Equations 216\u003c\/p\u003e \u003cp\u003eClosed-Form Solutions of Ordinary Differential Equations 218\u003c\/p\u003e \u003cp\u003eNumerical Solutions of Ordinary Differential Equations 222\u003c\/p\u003e \u003cp\u003eNonlinear Dynamics and Chaos 228\u003c\/p\u003e \u003cp\u003ePartial Differential Equations 231\u003c\/p\u003e \u003cp\u003eKey Points 237\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 10 Stochastic Integrals 239\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 240\u003c\/p\u003e \u003cp\u003eThe Intuition behind Stochastic Integrals 243\u003c\/p\u003e \u003cp\u003eBrownian Motion Defined 248\u003c\/p\u003e \u003cp\u003eProperties of Brownian Motion 254\u003c\/p\u003e \u003cp\u003eStochastic Integrals Defined 255\u003c\/p\u003e \u003cp\u003eSome Properties of Itoˆ Stochastic Integrals 259\u003c\/p\u003e \u003cp\u003eMartingale Measures and the Girsanov Theorem 260\u003c\/p\u003e \u003cp\u003eKey Points 266\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 11 Stochastic Differential Equations 267\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 268\u003c\/p\u003e \u003cp\u003eThe Intuition behind Stochastic Differential Equations 269\u003c\/p\u003e \u003cp\u003eItoˆ Processes 272\u003c\/p\u003e \u003cp\u003eStochastic Differential Equations 273\u003c\/p\u003e \u003cp\u003eGeneralization to Several Dimensions 276\u003c\/p\u003e \u003cp\u003eSolution of Stochastic Differential Equations 278\u003c\/p\u003e \u003cp\u003eDerivation of Itoˆ ’s Lemma 282\u003c\/p\u003e \u003cp\u003eDerivation of the Black-Scholes Option Pricing Formula 284\u003c\/p\u003e \u003cp\u003eKey Points 291\u003c\/p\u003e \u003cp\u003eIndex 293\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eSERGIO M. FOCARDI, P\u003csmall\u003eH\u003c\/small\u003eD,\u003c\/b\u003e is a Visiting Professor in the College of Business at the State University of New York at Stony Brook and founding partner of the Paris-based consulting firm The Intertek Group. He is a member of the editorial board of the \u003ci\u003eJournal of Portfolio Management\u003c\/i\u003e. Focardi has authored numerous articles and books on financial modeling and risk management and three monographs for the Research Foundation of the CFA Institute. \u003c\/p\u003e\u003cp\u003e\u003cb\u003eFRANK J. FABOZZI, P\u003csmall\u003eH\u003c\/small\u003eD, CFA,\u003c\/b\u003e is Professor of Finance at EDHEC Business School and a member of the EDHEC-Risk Institute. Prior to joining EDHEC in August 2011, he held various professorial positions in finance at Yale University’s School of Management from 1994 to 2011 and was a visiting professor of finance and accounting at MIT’s Sloan School of Management from 1986 to 1992. He is also Editor of the \u003ci\u003eJournal of Portfolio Management.\u003c\/i\u003e \u003c\/p\u003e\u003cp\u003e\u003cb\u003eTURAN G. BALI, P\u003csmall\u003eH\u003c\/small\u003eD,\u003c\/b\u003e is the Robert S. Parker Chair Professor of Business Administration at the McDonough School of Business at Georgetown University. Before joining Georgetown, Professor Bali was the David Krell Chair Professor of Finance at Baruch College and the Graduate School and University Center of the City University of New York. He also held visiting faculty positions at New York University and Princeton University. Professor Bali has published more than fifty articles in economics and finance journals. He is currently an associate editor of the \u003ci\u003eJournal of Banking and Finance, Journal of Futures Markets, Journal of Portfolio Management,\u003c\/i\u003e and \u003ci\u003eJournal of Risk\u003c\/i\u003e.    \u003c\/p\u003e\u003cp\u003eModern finance draws upon many fields of mathematics—from probability and statistics to stochastic calculus—and the level of mathematical skill needed to master today’s financial markets is extremely high.  \u003c\/p\u003e\u003cp\u003eNobody understands this better than the author team of Sergio Focardi, Frank Fabozzi, and Turan Bali. Now, in \u003ci\u003eMathematical Methods for Finance,\u003c\/i\u003e they draw upon their extensive experience in this important area in order to help both practitioners and students gain a firm understanding of the subject.  \u003c\/p\u003e\u003cp\u003eCovering a wide range of technical topics in mathematics and finance, this reliable resource opens with an informative discussion of three basic concepts—which are used in financial theory, financial modeling, and financial econometrics—found throughout the book: sets, functions, and variables. From there, it introduces and explains key mathematical techniques, ranging from differential and integral calculus, matrix algebra, and probability theory to difference and differential equations, optimization, and stochastic integrals. Page by page, you’ll discover how these techniques are successfully implemented in asset management and risk management. \u003c\/p\u003e\u003cp\u003eEach chapter begins with a brief description of how the tools and concepts covered are used in finance, followed by learning objectives. And a wealth of real-world examples—of how quantitative analysis is used in practice—skillfully highlights the connection between this analysis and financial decision-making. \u003c\/p\u003e\u003cp\u003eBridging the gap between the intuition of a practitioner and academic mathematical analysis, \u003ci\u003eMathematical Methods for Finance\u003c\/i\u003e is an essential guide for anyone who intends on exceling in today’s demanding world of finance.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989586460901,"sku":"NP9781118312636","price":135.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118312636.jpg?v=1761784705","url":"https:\/\/k12savings.com\/es\/products\/mathematical-methods-for-finance-isbn-9781118312636","provider":"K12savings","version":"1.0","type":"link"}