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(Ebook) Mathematics and statistics for financial risk management 2nd Edition by Michael Bernard Miller ISBN 1118757645 9781118757642

  • SKU: EBN-11896330
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Authors:Miller, Michael Bernard
Year:2014
Editon:2nd edition
Publisher:John Wiley and Sons
Language:english
File Size:30.59 MB
Format:pdf
ISBNS:9781118757642, 1118757645
Categories: Ebooks

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(Ebook) Mathematics and statistics for financial risk management 2nd Edition by Michael Bernard Miller ISBN 1118757645 9781118757642

(Ebook) Mathematics and statistics for financial risk management 2nd Edition by Michael Bernard Miller - Ebook PDF Instant Download/Delivery: 1118757645, 9781118757642
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ISBN 10: 1118757645 
ISBN 13: 9781118757642
Author: Michael Bernard Miller

Risk professionals, financial engineers, and corporate risk managers looking for FRM exam accreditation, professors and students.

Now in its second edition with more topics, more sample problems and more real world examples, this popular guide to financial risk management introduces readers to practical quantitative techniques for analyzing and managing financial risk. In a concise and easy-to-read style, each chapter 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 Web site includes interactive Excel spreadsheet examples and templates.

(Ebook) Mathematics and statistics for financial risk management 2nd Table of contents:

Part I: Mathematical Foundations

  • Chapter 1: Review of Basic Mathematics

    • Algebra and Functions

    • Exponents and Logarithms

    • Solving Equations

    • Series and Summations

    • Introduction to Calculus (Derivatives and Integrals)

    • Multivariable Calculus (Partial Derivatives)

    • Optimization (Unconstrained and Constrained)

  • Chapter 2: Linear Algebra for Financial Applications

    • Vectors and Matrices

    • Matrix Operations (Addition, Multiplication)

    • Determinants and Inverses

    • Systems of Linear Equations

    • Eigenvalues and Eigenvectors

    • Quadratic Forms

    • Applications in Portfolio Theory

  • Chapter 3: Differential Equations and Stochastic Calculus Primer

    • Ordinary Differential Equations (ODEs)

    • Partial Differential Equations (PDEs)

    • Introduction to Stochastic Processes

    • Brownian Motion and Wiener Processes

    • Itô's Lemma (Basic Introduction)

    • Stochastic Differential Equations (SDEs)

Part II: Probability Theory for Financial Risk

  • Chapter 4: Fundamentals of Probability

    • Basic Concepts (Sample Space, Events, Probability Rules)

    • Conditional Probability and Bayes' Theorem

    • Random Variables (Discrete and Continuous)

    • Probability Distributions (PMF, PDF, CDF)

    • Expected Value, Variance, and Standard Deviation

  • Chapter 5: Common Probability Distributions in Finance

    • Discrete Distributions (Bernoulli, Binomial, Poisson)

    • Continuous Distributions (Uniform, Exponential, Normal)

    • The Standard Normal Distribution

    • Log-Normal Distribution (Crucial for Asset Prices)

    • Student's t-Distribution

    • Chi-Squared Distribution

    • F-Distribution

  • Chapter 6: Multivariate Probability and Copulas

    • Joint, Marginal, and Conditional Distributions

    • Covariance and Correlation

    • Multivariate Normal Distribution

    • Introduction to Copulas (Capturing Dependence)

    • Applications in Portfolio Risk and CDOs

Part III: Statistical Foundations for Financial Risk Management

  • Chapter 7: Descriptive Statistics

    • Measures of Central Tendency (Mean, Median, Mode)

    • Measures of Dispersion (Range, Variance, Standard Deviation, Skewness, Kurtosis)

    • Quantiles and Percentiles

    • Data Visualization (Histograms, Box Plots)

  • Chapter 8: Inferential Statistics: Estimation and Hypothesis Testing

    • Sampling Distributions

    • Central Limit Theorem

    • Point Estimation and Confidence Intervals

    • Hypothesis Testing (Null and Alternative Hypotheses, Type I and Type II Errors, p-values)

    • Common Statistical Tests (t-tests, z-tests, Chi-squared tests)

  • Chapter 9: Regression Analysis

    • Simple Linear Regression

    • Multiple Linear Regression

    • Assumptions of Linear Regression

    • Interpreting Regression Output (R-squared, Coefficients, p-values)

    • Dummy Variables

    • Applications in Factor Models and Risk Premia

  • Chapter 10: Time Series Analysis

    • Characteristics of Financial Time Series (Stylized Facts)

    • Stationarity

    • Autocorrelation and Partial Autocorrelation

    • AR, MA, ARMA, ARIMA Models

    • Unit Roots and Cointegration (Basic Introduction)

    • Applications in Forecasting and Volatility Modeling

Part IV: Applications in Financial Risk Management

  • Chapter 11: Value at Risk (VaR) and Expected Shortfall (ES)

    • Definition and Calculation of VaR (Historical, Parametric, Monte Carlo)

    • Properties and Limitations of VaR

    • Expected Shortfall (Conditional VaR)

    • Backtesting VaR Models

  • Chapter 12: Volatility Modeling

    • Historical Volatility

    • Implied Volatility

    • ARCH and GARCH Models (Basic Concepts and Application)

    • Exponentially Weighted Moving Average (EWMA)

  • Chapter 13: Risk Measurement and Management

    • Credit Risk (Probability of Default, Loss Given Default, Exposure at Default)

    • Market Risk

    • Operational Risk

    • Stress Testing and Scenario Analysis

    • Regulatory Frameworks (Basel Accords - quantitative aspects)

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