Mathematical Methods for Finance - Tools for Asset and Risk Management

Informationen zum Autor 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-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-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 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 . Klappentext 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 finance* Offers the basic mathematical concepts that apply to the field of quantitative finance, from sets and distances to functions and variables* The book also includes information on calculus, matrix algebra, differential equations, stochastic integrals, and much more* Written 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. Zusammenfassung The mathematical and statistical tools needed in the rapidly growing quantitative finance field With 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. Inhaltsverzeichnis 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 ...

Inhaltsverzeichnis

Preface xi
 
About the Authors xvii
 
CHAPTER 1 Basic Concepts: Sets, Functions, and Variables 1
 
Introduction 2
 
Sets and Set Operations 2
 
Distances and Quantities 6
 
Functions 10
 
Variables 10
 
Key Points 11
 
CHAPTER 2 Differential Calculus 13
 
Introduction 14
 
Limits 15
 
Continuity 17
 
Total Variation 19
 
The Notion of Differentiation 19
 
Commonly Used Rules for Computing Derivatives 21
 
Higher-Order Derivatives 26
 
Taylor Series Expansion 34
 
Calculus in More Than One Variable 40
 
Key Points 41
 
CHAPTER 3 Integral Calculus 43
 
Introduction 44
 
Riemann Integrals 44
 
Lebesgue-Stieltjes Integrals 47
 
Indefinite and Improper Integrals 48
 
The Fundamental Theorem of Calculus 51
 
Integral Transforms 52
 
Calculus in More Than One Variable 57
 
Key Points 57
 
CHAPTER 4 Matrix Algebra 59
 
Introduction 60
 
Vectors and Matrices Defined 61
 
Square Matrices 63
 
Determinants 66
 
Systems of Linear Equations 68
 
Linear Independence and Rank 69
 
Hankel Matrix 70
 
Vector and Matrix Operations 72
 
Finance Application 78
 
Eigenvalues and Eigenvectors 81
 
Diagonalization and Similarity 82
 
Singular Value Decomposition 83
 
Key Points 83
 
CHAPTER 5 Probability: Basic Concepts 85
 
Introduction 86
 
Representing Uncertainty with Mathematics 87
 
Probability in a Nutshell 89
 
Outcomes and Events 91
 
Probability 92
 
Measure 93
 
Random Variables 93
 
Integrals 94
 
Distributions and Distribution Functions 96
 
Random Vectors 97
 
Stochastic Processes 100
 
Probabilistic Representation of Financial Markets 102
 
Information Structures 103
 
Filtration 104
 
Key Points 106
 
CHAPTER 6 Probability: Random Variables and Expectations 107
 
Introduction 109
 
Conditional Probability and Conditional Expectation 110
 
Moments and Correlation 112
 
Copula Functions 114
 
Sequences of Random Variables 116
 
Independent and Identically Distributed Sequences 117
 
Sum of Variables 118
 
Gaussian Variables 120
 
Appproximating the Tails of a Probability Distribution: Cornish-Fisher Expansion and Hermite Polynomials 123
 
The Regression Function 129
 
Fat Tails and Stable Laws 131
 
Key Points 144
 
CHAPTER 7 Optimization 147
 
Introduction 148
 
Maxima and Minima 149
 
Lagrange Multipliers 151
 
Numerical Algorithms 156
 
Calculus of Variations and Optimal Control Theory 161
 
Stochastic Programming 163
 
Application to Bond Portfolio: Liability-Funding Strategies 164
 
Key Points 178
 
CHAPTER 8 Difference Equations 181
 
Introduction 182
 
The Lag Operator L 183
 
Homogeneous Difference Equations 183
 
Recursive Calculation of Values of Difference Equations 192
 
Nonhomogeneous Difference Equations 195
 
Systems of Linear Difference Equations 201
 
Systems of Homogeneous Linear Difference Equations 202
 
Key Points 209
 
CHAPTER 9 Differential Equations 211
 
Introduction 212
 
Differential Equations Defined 213
 
Ordinary Differential Equations 213
 
Systems of Ordinary Differential Equations 216
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Produktdetails

• Autoren: Turan G Bali, Turan G. Bali, Frank Fabozzi, Frank J Fabozzi, Frank J. Fabozzi, Frank J. (School of Management Fabozzi, Sergio Focardi, Sergio M Focardi, Sergio M. Focardi, Sergio M. Fabozzi Focardi, Sm Focardi, FOCARDI SERGIO M
• Verlag: Wiley, John and Sons Ltd
• Sprache: Englisch
• Produktform: Fester Einband
• Erschienen: 05.11.2013
• EAN: 9781118312636
• ISBN: 978-1-118-31263-6
• Seiten: 320
• Serien: Frank J. Fabozzi Series; Frank J. Fabozzi; Frank J. Fabozzi; Frank J. Fabozzi Series
• Thema: Sozialwissenschaften, Recht,Wirtschaft > Wirtschaft > Betriebswirtschaft