Introductory Mathematics and Statistics for Islamic Finance: + Website

Praise for Introductory Mathematics and Statistics for Islamic Finance The authors have done a great service for those who are undertaking quantitative analysis, empirical research, and developing models in Islamic economics and finance. The strength of the book lies in the range of topics covered the richness of its logical presentation, easy to follow examples and most importantly, simplification of complex mathematical and statistical concepts. This is an essential book for the library of any researcher of Islamic finance. ZAMIR IQBAL, Lead Investment Officer, The World Bank, Washington, DC, USA This book is a very accessible introduction to mathematical and statistical modelling in Islamic finance. With minimum prerequisites for reading, it presents a clear and concise exposition of the fundamental analytical tools in economics and illustrates their applications to important topics in Islamic finance. Introductory Mathematics and Statistics for Islamic Finance is a timely and major contribution to the collective efforts currently underway to close the wide gap between theoretical and empirical research in Islamic finance. The authors are among the leading thinkers and voices in Islamic finance, and write from a depth of experience. NABIL MAGHREBI, Professor of Finance, Graduate School of Economics, Wakayama University, Japan Center for the Study of Finance and Insurance, Osaka University This book is an important contribution and a must–read for every student seeking knowledge in this particular area. It is also undeniably a great resource for lecturers, researchers and practitioners who are interested in Islamic finance and its conceptualization. The book provides useful mathematical and statistical tools for Islamic finance and presents a wide range of applications in a concise, relevant and pedagogical way. ADAMA DIEYE, Central Bank of the West African Economic and Monitory Union and Advisor in the Cabinet Ministry of Economy and Finance of Senegal A book written by two senior and well respected Islamic economists that will have an important impact in the field. This book will equip a new generation of researchers with quantitative muscles. Learning Islamic finance using another language (Mathematics and Statistics) is a great way to push you towards mastering the field. Since Mathematics and Statistics are the language of logic, this book is expected to enhance and deepen the readers understanding of Islamic finance. ABDULLAH Q. TURKISTANI, Dean, Islamic Economics Institute King Abdulaziz University, Saudi Arabia There are several books in the market on both Mathematics and Statistics. However, Introductory Mathematics and Statistics for Islamic Finance is unique in many respects. It addresses a specific target group: researchers and students in the field of Islamic financean industry with an impressive growth record and tremendous potential. This book puts the fundamental requirements for quantitative research in a simple yet rigorous enough style to meet professional research standards. Its selection of the most relevant topics from a broad array of computational mathematics and statistics, and use of explanatory examples for direct application in Islamic finance make this book handy and most practical. MUNAWAWAR IQBAL, Chief Editor, Journal of King Abdulaziz University: Islamic Economics , and Former Chief of Research, Islamic Banking Division, Islamic Research and Training Institute, Islamic Development Bank, Jeddah

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

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.