Abstract
The chapter provides an overview of the mathematics, statistics, and probabilities required to measure, analyze, and forecast risk. We discuss probability theory and statistical analysis, unbiased estimates, time-series math, linear regression, and nonlinear estimation techniques (including logit and probit models and neural networks). The chapter also provides an overview of hypothesis testing, optimization, and linear algebra. It includes a mathematical description for our many risk statistics such as marginal contribution to risk, value at risk, Sharpe ratio, information ratio, etc. We also discuss extreme value functions and the investigation of outliers.
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