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Full Description
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
Probability theory
Statistics
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.
Contents
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
