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Author Mirakhor, Abbas
Title Introductory Mathematics and Statistics for Islamic Finance
Imprint New York : John Wiley & Sons, Incorporated, 2014
©2014
book jacket
Edition 1st ed
Descript 1 online resource (498 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Note Introductory Mathematics and Statistics for Islamic Finance -- Contents -- Preface -- Acknowledgments -- About the Authors -- Part One: Mathematics -- Chapter 1: Elementary Mathematics -- BASIC MATHEMATICAL OBJECTS -- Real Numbers -- Complex Numbers -- Absolute Value of a Number -- Vectors and Arrays -- Angles and Directions -- Graphics -- Reporting Economic and Financial Data -- VARIABLES, MONOMIALS, BINOMIALS, AND POLYNOMIALS -- Monomials, Binomials, and Polynomials -- Polynomial Lags -- Identities -- Factorization of a Polynomial -- EQUATIONS -- EQUATIONS OF HIGHER ORDER -- SEQUENCES -- SERIES -- Convergence of a Series -- APPLICATIONS OF SERIES TO PRESENT VALUE OF ASSETS -- Applications of Series to Present Value Computation -- SUMMARY -- QUESTIONS -- Chapter 2: Functions and Models -- DEFINITION OF A FUNCTION -- Parametric Form of a Function -- FUNCTIONS AND MODELS IN ECONOMICS -- The Market Model: Demand and Supply Functions -- The Budget Constraint -- The Production Possibility Frontier (PPF) -- The Utility Function -- Production Function -- Other Functions in Economics -- FUNCTIONS AND MODELS IN FINANCE -- The Present Value Function -- The Capital Asset Pricing Model (CAPM) -- Payoff of a Futures Contract -- Payoff of an Option Contract -- Payoff to a Swap -- Price of an Option -- The Forward Exchange Rate -- MULTIVARIATE FUNCTIONS IN ECONOMICS AND FINANCE -- Parametric Representation -- Level Curves -- SUMMARY -- QUESTIONS -- Chapter 3: Differentiation and Integration of Functions -- DIFFERENTIATION -- DIFFERENTIATION RULES -- MAXIMUM AND MINIMUM OF A FUNCTION -- MEAN VALUE THEOREM -- POLYNOMIAL APPROXIMATIONS OF A FUNCTION: TAYLOR'S EXPANSION -- INTEGRATION -- Integration -- The First Fundamental Theorem of Calculus -- Second Fundamental Theorem of Calculus -- Change in Variables in Indefinite Integrals -- Double Integral
APPLICATIONS IN FINANCE: DURATION AND CONVEXITY OF A SUKUK -- Duration of a Sukuk -- Application of Taylor Expansion to the Convexity of Sukuk's Price -- SUMMARY -- QUESTIONS -- Chapter 4: Partial Derivatives -- DEFINITION AND COMPUTATION OF PARTIAL DERIVATIVES -- The Chain Rule -- Derivatives of Implicit Functions -- TOTAL DIFFERENTIAL OF A FUNCTION WITH MANY VARIABLES -- DIRECTIONAL DERIVATIVES -- GRADIENTS -- TANGENT PLANES AND NORMAL LINES -- Tangent Planes -- Normal Line -- EXTREMA OF FUNCTIONS OF SEVERAL VARIABLES -- EXTREMAL PROBLEMS WITH CONSTRAINTS -- Elimination Method -- Lagrange Method -- SUMMARY -- QUESTIONS -- Chapter 5: Logarithm, Exponential, and Trigonometric Functions -- LOGARITHM FUNCTIONS -- Logarithm Identities -- Change of Base -- The Natural Logarithmic Function -- THE EXPONENTIAL FUNCTION -- POWER SERIES OF LOGARITHMIC AND EXPONENTIAL FUNCTIONS -- GENERAL EXPONENTIAL AND LOGARITHMIC FUNCTIONS -- SOME APPLICATIONS OF LOGARITHM AND EXPONENTIAL FUNCTIONS IN FINANCE -- Simple Compounding and Continuous Compounding of Returns -- The Present Value Formula -- The Normal Distribution -- INTEGRATION BY PARTS -- TRIGONOMETRIC FUNCTIONS -- SUMMARY -- QUESTIONS -- Chapter 6: Linear Algebra -- VECTORS -- Addition of Vectors -- Multiplication of Vectors -- Vector Space -- Linear Combinations of Vectors -- Linear Dependence and Linear Independence of Vectors -- Bases of a Vector Space -- MATRICES -- Transposes of Matrices -- Matrix Multiplication -- SQUARE MATRICES -- Symmetric Matrix -- Positive Definite Matrix -- Quadratic Forms -- Orthogonal Matrix -- THE RANK OF A MATRIX -- DETERMINANT OF A SQUARE MATRIX -- HOMOGENOUS SYSTEMS OF EQUATIONS -- INVERSE AND GENERALIZED INVERSE MATRICES -- Generalized Inverse of a Matrix -- EIGENVALUES AND EIGENVECTORS -- Similarity of Square Matrices -- Diagonable Matrix -- Cholesky Decomposition
STABILITY OF A LINEAR SYSTEM -- APPLICATIONS IN ECONOMETRICS -- SUMMARY -- QUESTIONS -- Chapter 7: Differential Equations -- EXAMPLES OF DIFFERENTIAL EQUATIONS -- SOLUTION METHODS FOR THE DIFFERENTIAL EQUATION -- Method of Indefinite Integrals -- Method of Separable Variables -- FIRST-ORDER LINEAR DIFFERENTIAL EQUATIONS -- SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS -- Homogeneous Linear Differential Equation -- Nonhomogeneous Linear Differential Equations -- LINEAR DIFFERENTIAL EQUATION SYSTEMS -- Transforming the System into a Second-Order Homogeneous Differential Equation -- Method of Eigenvalues and Eigenvectors -- PHASE DIAGRAMS AND STABILITY ANALYSIS -- Phase Line of an Ordinary Differential Equation -- Phase Diagram of a Linear Differential Equation System -- SUMMARY -- QUESTIONS -- Chapter 8: Difference Equations -- DEFINITION OF A DIFFERENCE EQUATION -- FIRST-ORDER LINEAR DIFFERENCE EQUATIONS -- Solutions of the First-Order Difference Equation -- The Impulse Response Function -- The Cobweb Model -- SECOND-ORDER LINEAR DIFFERENCE EQUATIONS -- Homogeneous Second-Order Difference Equations -- Nonhomogeneous Second-Order Difference Equations -- The Multiplier-Accelerator Model -- SYSTEM OF LINEAR DIFFERENCE EQUATIONS -- EQUILIBRIUM AND STABILITY -- Conditions for Stability -- Stability of the Linear Difference System -- Phase Plane -- SUMMARY -- QUESTIONS -- Chapter 9: Optimization Theory -- THE MATHEMATICAL PROGRAMMING PROBLEM -- Formulation of the Programming Problem -- The Geometry of Optimization -- UNCONSTRAINED OPTIMIZATION -- One Variable Function y= F(x) -- Function of Two Variables z= F(x,y) -- Definitions -- CONSTRAINED OPTIMIZATION -- The Method of Lagrange Multipliers -- THE GENERAL CLASSICAL PROGRAM -- The Geometry of Constrained Optimization -- Interpretation of the Lagrangian Multipliers -- Nonlinear Programming
The Case of No Inequality Constraints -- The Kuhn-Tucker (K-T) Conditions -- SUMMARY -- QUESTIONS -- Chapter 10: Linear Programming -- FORMULATION OF THE LP -- Standard Form and Canonical Form of the LP -- The Geometry of the LP -- THE ANALYTICAL APPROACH TO SOLVING AN LP: THE SIMPLEX METHOD -- Notion of Technical Equivalence -- The Simplex Method -- THE DUAL PROBLEM OF THE LP -- THE LAGRANGIAN APPROACH: EXISTENCE, DUALITY, AND COMPLEMENTARY SLACKNESS THEOREMS -- Interpretation of the Dual Variables -- ECONOMIC THEORY AND DUALITY -- SUMMARY -- QUESTIONS -- Part Two: Statistics -- Chapter 11: Introduction to Probability Theory: Axioms and Distributions -- THE EMPIRICAL BACKGROUND: THE SAMPLE SPACE AND EVENTS -- Experiment -- Sample Space -- Events -- DEFINITION OF PROBABILITY -- Axioms of Probability -- RANDOM VARIABLE -- TECHNIQUES OF COUNTING: COMBINATORIAL ANALYSIS -- Factorial Notation -- Permutations -- Ordered Samples -- Combinations -- Tree Diagrams -- CONDITIONAL PROBABILITY AND INDEPENDENCE -- Conditional Probability -- Bayes' Theorem -- Independence of Events -- PROBABILITY DISTRIBUTION OF A FINITE RANDOM VARIABLE -- Probability Distribution and Histogram -- Cumulative Distribution Function -- Continuous Random Variables -- MOMENTS OF A PROBABILITY DISTRIBUTION -- First Moment of the Random Variable -- Second Moment of the Random Variable: Variance and Standard Deviation -- Third Moment of a Random Variable: Skewness -- Fourth Moment of a Random Variable: Kurtosis -- JOINT DISTRIBUTION OF RANDOM VARIABLES -- Independent Random Variables -- CHEBYSHEV'S INEQUALITY AND THE LAW OF LARGE NUMBERS -- Chebyshev's Inequality -- Law of Large Numbers -- The Central Limit Theorem -- SUMMARY -- QUESTIONS -- Chapter 12: Probability Distributions and Moment Generating Functions -- EXAMPLES OF PROBABILITY DISTRIBUTIONS -- The Uniform Distribution
The Bernoulli Distribution -- The Binomial Distribution -- The Poisson Distribution -- The Normal Distribution -- The Chi-Square Distribution -- The t Distribution -- The F Distribution -- EMPIRICAL DISTRIBUTIONS -- MOMENT GENERATING FUNCTION (MGF) -- Examples of Moment Generating Functions -- SUMMARY -- QUESTIONS -- Chapter 13: Sampling and Hypothesis Testing Theory -- SAMPLING DISTRIBUTIONS -- Sampling Distribution of the Mean -- Sampling Distribution of Proportions -- Sampling Distribution of Differences -- ESTIMATION OF PARAMETERS -- Unbiased Estimates -- Efficient Estimates -- Point Estimates and Interval Estimates -- CONFIDENCE-INTERVAL ESTIMATES OF POPULATION PARAMETERS -- Confidence Intervals for Means -- Confidence Intervals for Proportions -- Confidence Intervals for Differences -- Confidence Intervals for Standard Deviations -- HYPOTHESIS TESTING -- Statistical Hypotheses -- Null Hypotheses -- Alternative Hypothesis -- Type I and Type II Errors -- Level of Significance -- Probability Value: p-Value -- Special Tests -- Means -- Proportions -- TESTS INVOLVING SAMPLE DIFFERENCES -- SMALL SAMPLING THEORY -- Tests Based on the Student's t-Distribution -- Confidence Intervals for t Distribution -- Tests Based on the Chi-Square Distribution -- Confidence Intervals for χ² -- Tests Based on the F Distribution -- SUMMARY -- QUESTIONS -- Chapter 14: Regression Analysis -- CURVE FITTING -- Equations of Approximating Curves -- The Linear Regression Line -- The Principle of Estimation: Method of Least Squares -- LINEAR REGRESSION ANALYSIS -- Formulation of the Regression Model -- Estimation of the Regression Model -- The Method of Moments -- The Method of the Maximum Likelihood -- Estimate of the Variance of the Error Term -- The Coefficient of Determination and the Coefficient of Correlation
THE PROBABILITY DISTRIBUTION OF THE ESTIMATED REGRESSION COEFFICIENTS â AND b
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
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Mirakhor, Abbas Introductory Mathematics and Statistics for Islamic Finance New York : John Wiley & Sons, Incorporated,c2014 9781118779699
Subject Finance (Islamic law);Finance -- Islamic countries
Electronic books
Alt Author Krichene, Noureddine
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