Mathematics and statistics for financial risk management / Michael B. Miller

Preface -- Acknowledgments -- CHAPTER 1. Some Basic Math -- Logarithms -- Log Returns -- Compounding -- Limited Liability -- Graphing Log Returns -- Continuously Compounded Returns -- Combinatorics -- Discount Factors -- Geometric Series -- Problems -- CHAPTER 2 Probabilities -- Discrete Random Variables -- Continuous Random Variables -- Mutually Exclusive Events -- Independent Events -- Probability Matrices -- Conditional Probability -- Bayes' Theorem -- Problems -- CHAPTER 3. Basic Statistics -- Averages -- Expectations -- Variance and Standard Deviation -- Standardized Variables -- Covariance -- Correlation -- Application: Portfolio Variance and Hedging -- Moments -- Skewness -- Kurtosis -- Coskewness and Cokurtosis -- Best Linear Unbiased Estimator (BLUE) -- Problems -- CHAPTER 4 Distributions -- Parametric Distributions -- Uniform Distribution -- Bernoulli Distribution -- Binomial Distribution -- Poisson Distribution -- Normal Distribution -- Lognormal Distribution -- Central Limit Theorem -- Application: Monte Carlo Simulations Part I: Creating Normal Random Variables -- Chi-Squared Distribution -- Student's t Distribution -- F -Distribution -- Mixture Distributions -- Problems -- CHAPTER 5 Hypothesis Testing & Confidence Intervals -- The Sample Mean Revisited -- Sample Variance Revisited -- Confidence Intervals -- Hypothesis Testing -- Chebyshev's Inequality -- Application: VaR -- Problems -- CHAPTER 6 Matrix Algebra -- Matrix Notation -- Matrix Operations -- Application: Transition Matrices -- Application: Monte Carlo Simulations Part II: Cholesky Decomposition -- Problems -- CHAPTER 7 Vector Spaces -- Vectors Revisited -- Orthogonality -- Rotation -- Principal Component Analysis -- Application: The Dynamic Term Structure of Interest Rates -- Application: The Structure of Global Equity Markets -- Problems -- CHAPTER 8 Linear Regression Analysis -- Linear Regression (One Regressor) -- Linear Regression (Multivariate) -- Application: Factor Analysis -- Application: Stress Testing -- Problems -- CHAPTER 9 Time Series Models -- Random Walks -- Drift-Diffusion -- Autoregression -- Variance and Autocorrelation -- Stationarity -- Moving Average -- Continuous Models -- Application: GARCH -- Application: Jump-Diffusion -- Application: Interest Rate Models -- Problems -- CHAPTER 10 Decay Factors -- Mean -- Variance -- Weighted Least Squares -- Other Possibilities -- Application: Hybrid VaR -- Problems -- APPENDIX A Binary Numbers -- APPENDIX B Taylor Expansions -- APPENDIX C Vector Spaces -- APPENDIX D Greek Alphabet -- APPENDIX E Common Abbreviations -- Answers -- References -- About the Author -- Index.

Mathematics and Statistics for Financial Risk Management is a practical guide to modern financial risk management for both practitioners and academics. The recent financial crisis and its impact on the broader economy underscore the importance of financial risk management in today's world.