Quantitative Methods by Brandimarte, Paolo -- Read -- Imperial Library of Trantor

Index

Cover Half Title page Title page Copyright page Preface Part I: Motivations and Foundations

Chapter 1: Quantitative Methods: Should We Bother?

1.1 A Decision Problem Without Uncertainty: Product Mix 1.2 The Role of Uncertainty 1.3 Endogenous vs. Exogenous Uncertainty: Are We Alone? 1.4 Quantitative Models and Methods 1.5 Quantitative Analysis and Problem Solving References

Chapter 2: Calculus

2.1 A Motivating Example: Economic Order Quantity 2.2 A Little Background 2.3 Functions 2.4 Continuous Functions 2.5 Composite Functions 2.6 Inverse Functions 2.7 Derivatives 2.8 Rules for Calculating Derivatives 2.9 Using Derivatives for Graphing Functions 2.10 Higher-Order Derivatives and Taylor Expansions 2.11 Convexity and Optimization 2.12 Sequences and Series 2.13 Definite Integrals References

Chapter 3: Linear Algebra

3.1 A Motivating Example: Binomial Option Pricing 3.2 Solving Systems of Linear Equations 3.3 Vector Algebra 3.4 Matrix Algebra 3.5 Linear Spaces 3.6 Determinant 3.7 Eigenvalues and Eigenvectors 3.8 Quadratic Forms 3.9 Calculus in Multiple Dimensions References

Part II: Elementary Probability and Statistics

4.1 What Is Statistics? 4.2 Organizing and Representing Raw Data 4.3 Summary Measures 4.4 Cumulative Frequencies and Percentiles 4.5 Multidimensional Data References

Chapter 5: Probability Theories

5.1 Different Concepts of Probability 5.2 The Axiomatic Approach 5.3 Conditional Probability and Independence 5.4 Total Probability and Bayes’ Theorems References

Chapter 6: Discrete Random Variables

6.1 Random Variables 6.2 Characterizing Discrete Distributions 6.3 Expected Value 6.4 Variance and Standard Deviation 6.5 A Few Useful Discrete Distributions References

Chapter 7: Continuous Random Variables

7.1 Building Intuition: From Discrete to Continuous Random Variables 7.2 Cumulative Distribution and Probability Density Functions 7.3 Expected Value and Variance 7.4 Mode, Median, and Quantiles 7.5 Higher-Order Moments, Skewness, and Kurtosis 7.6 A Few Useful Continuous Probability Distributions 7.7 Sums of Independent Random Variables 7.8 Miscellaneous Applications 7.9 Stochastic Processes 7.10 Probability Spaces, Measurability, and Information References

Chapter 8: Dependence, Correlation, and Conditional Expectation

8.1 Joint and Marginal Distributions 8.2 Independent Random Variables 8.3 Covariance and Correlation 8.4 Jointly Normal Variables 8.5 Conditional Expectation References

Chapter 9: Inferential Statistics

9.1 Random Samples and Sample Statistics 9.2 Confidence Intervals 9.3 Hypothesis Testing 9.4 Beyond The Mean of One Population 9.5 Checking The Fit of Hypothetical Distributions: The Chi-Square Test 9.6 Analysis of Variance 9.7 Monte Carlo Simulation 9.8 Stochastic Convergence and The Law of Large Numbers 9.9 Parameter Estimation 9.10 Some More Hypothesis Testing Theory References

Chapter 10: Simple Linear Regression

10.1 Least-Squares Method 10.2 The Need for A Statistical Framework 10.3 The Case of A Nonstochastic Regressor 10.4 Using Regression Models 10.5 A Glimpse of Stochastic Regressors and Heteroskedastic Errors 10.6 A Vector Space Look at Linear Regression References

Chapter 11: Inferential Statistics

11.1 Before We Start: Framing The Forecasting Process 11.2 Measuring Forecast Errors 11.3 Time Series Decomposition 11.4 Moving Average 11.5 Heuristic Exponential Smoothing 11.6 A Glance At Advanced Time Series Modeling References

Part III: Models for Decision Making

Chapter 12: Deterministic Decision Models

12.1 A Taxonomy of Optimization Models 12.2 Building Linear Programming Models 12.3 A Repertoire of Model Formulation Tricks 12.4 Building Integer Programming Models 12.5 Nonlinear Programming Concepts 12.6 A Glance At Solution Methods References

Chapter 13: Decision Making Under Risk

13.1 Decision Trees 13.2 Risk Aversion and Risk Measures 13.3 Two-Stage Stochastic Programming Models 13.4 Multistage Stochastic Linear Programming With Recourse 13.5 Robustness, Regret, and Disappointment References

Chapter 14: Multiple Decision Makers, Subjective Probability, and Other Wild Beasts

14.1 What Is Uncertainty? 14.2 Decision Problems with Multiple Decision Makers 14.3 Incentive Misalignment in Supply Chain Management 14.4 Game Theory 14.5 Braess’ Paradox for Traffic Networks 14.6 Dynamic Feedback Effects and Herding Behavior 14.7 Subjective Probability: The Bayesian View References

Part IV: Advanced Statistical Modeling

Chapter 15: Introduction to Multivariate Analysis

15.1 Issues in Multivariate Analysis 15.2 An Overview of Multivariate Methods 15.3 Matrix Algebra and Multivariate Analysis References

Chapter 16: Advanced Regression Models

16.1 Multiple Linear Regression by Least Squares 16.2 Building, Testing, and Using Multiple Linear Regression Models 16.3 Logistic Regression 16.4 A Glance At Nonlinear Regression References

Chapter 17: Dealing with Complexity: Data Reduction and Clustering

17.1 The Need for Data Reduction 17.2 Principal Component Analysis (PCA) 17.3 Factor Analysis 17.4 Cluster Analysis References

Index