A unique and indispensable pocket guide to concepts at the heart of professional risk management, this book explains the complex concepts of risk mathematics and gives auditors a confident, conceptual understanding of risk mathematics and the ability to spot mistakes. It introduces a series of ideas and terms about the mathematics of risk, using accessible language and keeping formulae to a minimum.
Start here. Good choice! This book. How this book works. The myth of mathematical clarity. The myths of quantification. The auditor's mission. Auditing simple risk assessments. 1 Probabilities. 2 Probabilistic forecaster. 3 Calibration (also known as reliability). 4 Resolution. 5 Proper score function. 6 Audit point: Judging probabilities. 7 Probability interpretations. 8 Degree of belief. 9 Situation (also known as an experiment). 10 Long run relative frequency. 11 Degree of belief about long run relative frequency. 12 Degree of belief about an outcome. 13 Audit point: Mismatched interpretations of probability. 14 Audit point: Ignoring uncertainty about probabilities. 15 Audit point: Not using data to illuminate probabilities. 16 Outcome space (also known as sample space, or possibility space). 17 Audit point: Unspecified situations. 18 Outcomes represented without numbers. 19 Outcomes represented with numbers. 20 Random variable. 21 Event. 22 Audit point: Events with unspecified boundaries. 23 Audit point: Missing ranges. 24 Audit point: Top 10 risk reporting. 25 Probability of an outcome. 26 Probability of an event. 27 Probability measure (also known as probability distribution, probability function, or even probability distribution function). 28 Conditional probabilities. 29 Discrete random variables. 30 Continuous random variables. 31 Mixed random variables (also known as mixed discrete-continuous random variables). 32 Audit point: Ignoring mixed random variables. 33 Cumulative probability distribution function. 34 Audit point: Ignoring impact spread. 35 Audit point: Confusing money and utility. 36 Probability mass function. 37 Probability density function. 38 Sharpness. 39 Risk. 40 Mean value of a probability distribution (also known as the expected value). 41 Audit point: Excessive focus on expected values. 42 Audit point: Misunderstanding 'expected'. 43 Audit point: Avoiding impossible provisions. 44 Audit point: Probability impact matrix numbers. 45 Variance. 46 Standard deviation. 47 Semi-variance. 48 Downside probability. 49 Lower partial moment. 50 Value at risk (VaR). 51 Audit point: Probability times impact. Some types of probability distribution. 52 Discrete uniform distribution. 53 Zipf distribution. 54 Audit point: Benford's law. 55 Non-parametric distributions. 56 Analytical expression. 57 Closed form (also known as a closed formula or explicit formula). 58 Categorical distribution. 59 Bernoulli distribution. 60 Binomial distribution. 61 Poisson distribution. 62 Multinomial distribution. 63 Continuous uniform distribution. 64 Pareto distribution and power law distribution. 65 Triangular distribution. 66 Normal distribution (also known as the Gaussian distribution). 67 Audit point: Normality tests. 68 Non-parametric continuous distributions. 69 Audit point: Multi-modal distributions. 70 Lognormal distribution. 71 Audit point: Thin tails. 72 Joint distribution. 73 Joint normal distribution. 74 Beta distribution. Auditing the design of business prediction models. 75 Process (also known as a system). 76 Population. 77 Mathematical model. 78 Audit point: Mixing models and registers. 79 Probabilistic models (also known as stochastic models or statistical models). 80 Model structure. 81 Audit point: Lost assumptions. 82 Prediction formulae. 83 Simulations. 84 Optimization. 85 Model inputs. 86 Prediction formula structure. 87 Numerical equation solving. 88 Prediction algorithm. 89 Prediction errors. 90 Model uncertainty. 91 Audit point: Ignoring model uncertainty. 92 Measurement uncertainty. 93 Audit point: Ignoring measurement uncertainty. 94 Audit point: Best guess forecasts. 95 Prediction intervals. 96 Propagating uncertainty. 97 Audi
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