05967nmm a2200541 u 4500001001200000003002700012005001700039007002400056008004100080020001800121020001500139050000900154100002000163245010100183250001600284260002800300300001100328505016300339505005000502505059900552505022201151505059001373505057601963505058102539653004903120653004203169653004803211653004503259653004203304653004703346041001903393989002203412490001803434500006203452776001803514776001803532776001503550776001803565776001803583856008403601082000803685082001603693082000803709082000803717082000803725082001203733520168003745EB001933950EBX0100000000000000109685200000000000000.0cr|||||||||||||||||||||210123 ||| eng a9781118227770 a1118227778 4aHD611 aMiller, Michael00aMathematics and Statistics for Financial Risk Managementh[electronic resource]cMiller, Michael a1st edition bJohn Wiley & Sonsc2012 a304 p.0 aAPPENDIX B Taylor ExpansionsAPPENDIX C Vector Spaces; APPENDIX D Greek Alphabet; APPENDIX E Common Abbreviations; Answers; References; About the Author; Index0 aIncludes bibliographical references and index0 aCHAPTER 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; Problems0 aSome basic math -- Probabilities -- Basic statistics -- Distribution -- Hypothesis testing & confidence intervals -- Matrix algebra -- Vector spaces -- Linear regression analysis -- Time series models -- Decay factors0 aStandardized 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; Problems0 aCHAPTER 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 Numbers0 aMathematics 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 aRisk management / Mathematical models / fast aRisk management / Mathematical models aGestion du risque / Modèles mathématiques aBUSINESS & ECONOMICS / Finance / bisacsh aRisk management / Statistical methods aGestion du risque / Méthodes statistiques07aeng2ISO 639-2 bOREILLYaO'Reilly0 aWiley finance aMade available through: Safari, an O'Reilly Media Company z9781118244197 z9781118227770 z1118170628 z9781118170625 z978111823976640uhttps://learning.oreilly.com/library/view/~/9781118170625/?arxVerlag3Volltext0 a6580 a332.01/51950 a3680 a3320 a3300 a658.155 aMathematics 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 the same time, financial products and investment strategies are becoming increasingly complex. Today, it is more important than ever that risk managers possess a sound understanding of mathematics and statistics. In a concise and easy-to-read style, each chapter of this book introduces a different topic in mathematics or statistics. As different techniques are introduced, sample problems and application sections demonstrate how these techniques can be applied to actual risk management problems. Exercises at the end of each chapter and the accompanying solutions at the end of the book allow readers to practice the techniques they are learning and monitor their progress. A companion website includes interactive Excel spreadsheet examples and templates. This comprehensive resource covers basic statistical concepts from volatility and Bayes' Law to regression analysis and hypothesis testing. Widely used risk models, including Value-at-Risk, factor analysis, Monte Carlo simulations, and stress testing are also explored. A chapter on time series analysis introduces interest rate modeling, GARCH, and jump-diffusion models. Bond pricing, portfolio credit risk, optimal hedging, and many other financial risk topics are covered as well. If you're looking for a book that will help you understand the mathematics and statistics of financial risk management, look no further