Mathematics and Statistics for Financial Risk Management

Key differences between 2nd and 1st editions

• Time lapse between current and previous editions: 1 year (2013 vs 2012).
• The First edition of Miller's statistics textbook was published in 2012.
• Chapter 4: New discussions on Triangular and Beta Distributions, which can be used to model default rates and recovery rates.
• New Chapter 5 "Multivariate Distributions and Copulas" investigates concepts for measuring the risk of portfolios, including joint distributions and copulas.
• Section "Multivariate Distributions" covers discrete distributions, continuous joint distributions, visualization of probability density function in three dimensions, correlation, and marginal distributions.
• Section "Copulas" covers definition of copula (a multivariate probability distribution), graphing copulas, how copulas can be used in Monte Carlo simulations, and parameterization of copulas.
• New Chapter 6 "Bayesian Analysis" covers:
• Bayes' theorem -- the foundation of Bayesian analysis.
• Comparison of Bayes vs Frequentists approach - which approach is better?
• Many-State problems -- extension of Bayesian analysis to any number of possible outcomes.
• Continuous distributions
• Bayesian networks -- representation of the causal relationships between different random variables.
• Comparison of Bayesian networks vs correlation matrices.
• New Appendix F "Copulas" summarizes the properties of various named copulas.