### Mathematics and Statistics for Financial Risk Management

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. At t...

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Main Author: eBook English John Wiley & Sons 2012 1st edition Wiley finance O'Reilly - Collection details see MPG.ReNa
• APPENDIX B Taylor ExpansionsAPPENDIX C Vector Spaces; APPENDIX D Greek Alphabet; APPENDIX E Common Abbreviations; Answers; References; About the Author; Index
• Includes bibliographical references and index
• CHAPTER 5 Hypothesis Testing & Confidence IntervalsThe 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
• Some basic math
• Probabilities
• Basic statistics
• Distribution
• Hypothesis testing & confidence intervals
• Matrix algebra
• Vector spaces
• Linear regression analysis
• Time series models
• Decay factors
• Standardized VariablesCovariance; 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 8 Linear Regression AnalysisLinear 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
• Mathematics andStatistics for FinancialRisk Management; Contents; 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