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

##### By: Miller, Michael B. (Michael Bernard).

Material type: BookSeries: Wiley finance series: Publisher: Hoboken, N.J. : Wiley, 2012Description: 1 online resource (xi, 281 pages) : illustrations.Content type: text Media type: computer Carrier type: online resourceISBN: 9781118227770; 1118227778; 9781118239766; 1118239768; 1280588969; 9781280588969; 9781118819616; 1118819616; 1306207916; 9781306207911.Subject(s): Risk management -- Mathematical models | Risk management -- Statistical methods | Reference & resource series | BUSINESS & ECONOMICS -- Finance | BusinessGenre/Form: Electronic books.Additional physical formats: Print version:: Mathematics and statistics for financial risk management.DDC classification: 332.01/5195 Other classification: BUS027000 Online resources: Wiley Online LibraryIncludes bibliographical references and index.

Some basic math -- Probabilities -- Basic statistics -- Distribution -- Hypothesis testing & confidence intervals -- Matrix algebra -- Vector spaces -- Linear regression analysis -- Time series models -- Decay factors.

"In chapter 1, there is a review three math topics -- logarithms, combinatorics, and geometric series - and one financial topic, discount factors. Emphasis will be given to the specific aspects of these topics that are most relevant to risk management. In chapter 2, the author explores the application of probabilities to risk management. There is also an introduction to basic terminology and notations that will be used throughout the rest of the book. In chapter 3, Miller teaches how to describe a collection of data in precise statistical terms. Many of the concepts will be familiar, but the notation and terminology might be new. This notation and terminology will be used throughout the rest of the book. In chapter 4, some of the most common probability distributions will be pointed out, followed by a chapter on two closely related topics, confidence intervals and hypothesis testing. For risk management, these are possibly the two most important concepts in statistics. Chapter 6 provides a basic introduction to linear regression models. At the end of the chapter, Miller explores two risk management applications, factor analysis and stress testing. The final chapter is on a class of estimators, which has become very popular in finance and risk management for analyzing historical data. These models hint at the limitations of the type of analysis that we have been explores in previous chapters. This book has a lot of charts and equations"-- Provided by publisher.

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.

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 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.

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.

APPENDIX B Taylor ExpansionsAPPENDIX C Vector Spaces; APPENDIX D Greek Alphabet; APPENDIX E Common Abbreviations; Answers; References; About the Author; Index.

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