A unique primer on quantitative methods as applied to Islamic finance
Introductory Mathematics and Statistics for Islamic Finance + Website is a comprehensive guide to quantitative methods, specifically as applied within the realm of Islamic finance. With applications based on research, the book provides readers with the working knowledge of math and statistics required to understand Islamic finance theory and practice. The numerous worked examples give students with various backgrounds a uniform set of common tools for studying Islamic finance.
The in-depth study of finance requires a strong foundation in quantitative methods. Without a good grasp of math, probability, and statistics, published theoretical and applied works in Islamic finance remain out of reach. Unlike a typical math text, this book guides students through only the methods that directly apply to Islamic finance, without wasting time on irrelevant techniques. Each chapter contains a detailed explanation of the topic at hand, followed by an example based on real situations encountered in Islamic finance. Topics include:
Algebra and matrices
Calculus and differential equations
Written by leading experts on the subject, the book serves as a useful primer on the analysis methods and techniques students will encounter in published research, as well as day-to-day operations in finance. Anyone aspiring to be successful in Islamic finance needs these skills, and Introductory Mathematics and Statistics for Islamic Finance + Website is a clear, concise, and highly relevant guide.
ABBAS MIRAKHOR is first Chair of Islamic Finance at the International Center for Education in Islamic Finance (INCEIF). Formerly, he served as Dean of the Executive Board of the International Monetary Fund (IMF) and as Executive Director representing Afghanistan, Algeria, Ghana, Iran, Morocco, Pakistan, and Tunisia. NOUREDDINE KRICHENE taught Islamic finance at INCEIF, Malaysia, was an economist with the International Monetary Fund, and acted as an advisor to the Islamic Development Bank in Saudi Arabia.
Preface ix Acknowledgments xi About the Authors xiii PART ONE Mathematics CHAPTER 1 Elementary Mathematics 3 CHAPTER 2 Functions and Models 25 CHAPTER 3 Differentiation and Integration of Functions 41 CHAPTER 4 Partial Derivatives 61 CHAPTER 5 Logarithm, Exponential, and Trigonometric Functions 77 CHAPTER 6 Linear Algebra 91 CHAPTER 7 Differential Equations 117 CHAPTER 8 Difference Equations 141 CHAPTER 9 Optimization Theory 167 CHAPTER 10 Linear Programming 195 PART TWO Statistics CHAPTER 11 Introduction to Probability Theory: Axioms and Distributions 227 CHAPTER 12 Probability Distributions and Moment Generating Functions 251 CHAPTER 13 Sampling and Hypothesis Testing Theory 271 CHAPTER 14 Regression Analysis 301 CHAPTER 15 Time Series Analysis 327 CHAPTER 16 Nonstationary Time Series and Unit-Root Testing 355 CHAPTER 17 Vector Autoregressive Analysis (VAR) 369 CHAPTER 18 Co-Integration: Theory and Applications 381 CHAPTER 19 Modeling Volatility: ARCH-GARCH Models 397 CHAPTER 20 Asset Pricing under Uncertainty 413 CHAPTER 21 The Consumption-Based Pricing Model 439 CHAPTER 22 Brownian Motion, Risk-Neutral Processes, and the Black-Scholes Model 451 References 473 Index 475