Abbas Mirakhor & Noureddine Krichene 
Introductory Mathematics and Statistics for Islamic Finance 

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.

Table of Content

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

About the author

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.