Mathematical Methods for Finance

Sergio M. Focardi 지음

Wiley 2013년 09월 04일 출간

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The mathematical and statistical tools needed in the rapidly growing quantitative finance fieldWith the rapid growth in quantitative finance, practitioners must achieve a high level of proficiency in math and statistics. Mathematical Methods and Statistical Tools for Finance, 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.It 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.Includes an overview of the essential math and statistical skills required to succeed in quantitative financeOffers the basic mathematical concepts that apply to the field of quantitative finance, from sets and distances to functions and variablesThe book also includes information on calculus, matrix algebra, differential equations, stochastic integrals, and much moreWritten by Sergio Focardi, one of the world's leading authors in high-level financeDrawing 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.

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Preface xiAbout the Authors xviiCHAPTER 1 Basic Concepts: Sets, Functions, and Variables 1Introduction 2Sets and Set Operations 2Distances and Quantities 6Functions 10Variables 10Key Points 11CHAPTER 2 Differential Calculus 13Introduction 14Limits 15Continuity 17Total Variation 19The Notion of Differentiation 19Commonly Used Rules for Computing Derivatives 21Higher-Order Derivatives 26Taylor Series Expansion 34Calculus in More Than One Variable 40Key Points 41CHAPTER 3 Integral Calculus 43Introduction 44Riemann Integrals 44Lebesgue-Stieltjes Integrals 47Indefinite and Improper Integrals 48The Fundamental Theorem of Calculus 51Integral Transforms 52Calculus in More Than One Variable 57Key Points 57CHAPTER 4 Matrix Algebra 59Introduction 60Vectors and Matrices Defined 61Square Matrices 63Determinants 66Systems of Linear Equations 68Linear Independence and Rank 69Hankel Matrix 70Vector and Matrix Operations 72Finance Application 78Eigenvalues and Eigenvectors 81Diagonalization and Similarity 82Singular Value Decomposition 83Key Points 83CHAPTER 5 Probability: Basic Concepts 85Introduction 86Representing Uncertainty with Mathematics 87Probability in a Nutshell 89Outcomes and Events 91Probability 92Measure 93Random Variables 93Integrals 94Distributions and Distribution Functions 96Random Vectors 97Stochastic Processes 100Probabilistic Representation of Financial Markets 102Information Structures 103Filtration 104Key Points 106CHAPTER 6 Probability: Random Variables and Expectations 107Introduction 109Conditi

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저자(글) Sergio M. Focardi

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SERGIO M. FOCARDI, PhD, 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#45;based consulting firm The Intertek Group. He is a member of the editorial board of the Journal of Portfolio Management. Focardi has authored numerous articles and books on financial modeling and risk management and three monographs for the Research Foundation of the CFA Institute.FRANK J. FABOZZI, PhD, CFA, is Professor of Finance at EDHEC Business School and a member of the EDHEC#45;Risk Institute. Prior to joining EDHEC in August 2011, he held various professorial positions in finance at Yale University#39;s School of Management from 1994 to 2011 and was a visiting professor of finance and accounting at MIT#39;s Sloan School of Management from 1986 to 1992. He is also Editor of the Journal of Portfolio Management.TURAN G. BALI, PhD, 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 Journal of Banking and Finance, Journal of Futures Markets, Journal of Portfolio Management, and Journal of Risk.