## A Pocket Guide to Risk Mathematics: Key Concepts Every Auditor Should KnowThis uniquely accessible, breakthrough book lets auditors grasp the thinking behind the mathematical approach to risk without doing the mathematics. Risk control expert and former Big 4 auditor, Matthew Leitch, takes the reader gently but quickly through the key concepts, explaining mistakes organizations often make and how auditors can find them. Spend a few minutes every day reading this conveniently pocket sized book and you will soon transform your understanding of this highly topical area and be in demand for interesting reviews with risk at their heart. "I was really excited by this book - and I am not a mathematician. With my basic understanding of business statistics and business risk management I was able to follow the arguments easily and pick up the jargon of a discipline akin to my own but not my own." |

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### Contents

1 | |

2 | |

How this book works | 3 |

The myth of mathematical clarity | 5 |

The myths of quantification | 7 |

The auditors mission | 8 |

Auditing simple risk assessments | 11 |

Probabilities | 12 |

Model structure | 88 |

Lost assumptions | 89 |

Simulations | 90 |

Prediction formula structure | 91 |

Numerical equation solving | 93 |

Prediction algorithm | 94 |

Ignoring model uncertainty | 95 |

Measurement uncertainty | 96 |

Probabilistic forecaster | 13 |

Resolution | 14 |

Proper score function | 15 |

Judging probabilities | 17 |

Degree of belief | 18 |

Situation also known as an experiment | 19 |

Long run relative frequency | 20 |

Degree of belief about long run relative frequency | 21 |

Degree of belief about an outcome | 22 |

Mismatched interpretations of probability | 24 |

Ignoring uncertainty about probabilities | 25 |

Outcome space also known as sample space or possibility space | 26 |

Unspecified situations | 27 |

Outcomes represented without numbers | 28 |

Outcomes represented with numbers | 29 |

Event | 30 |

Events with unspecified boundaries | 31 |

Missing ranges | 32 |

Probability of an outcome | 33 |

Probability of an event | 34 |

Conditional probabilities | 36 |

Discrete random variables | 37 |

Continuous random variables | 38 |

Mixed random variables also known as mixed discretecontinuous random variables | 39 |

Ignoring mixed random variables | 40 |

Cumulative probability distribution function | 41 |

Ignoring impact spread | 43 |

Confusing money and utility | 44 |

Probability density function | 45 |

Sharpness | 47 |

Risk | 49 |

Mean value of a probability distribution also known as the expected value | 50 |

Excessive focus on expected values | 51 |

Avoiding impossible provisions | 52 |

Probability impact matrix numbers | 53 |

Variance | 54 |

Standard deviation | 55 |

Lower partial moment | 56 |

Probability times impact | 58 |

some types of probability distribution | 61 |

Discrete uniform distribution | 62 |

Benfords law | 64 |

Nonparametric distributions | 65 |

Closed form also known as a closed formula or explicit formula | 66 |

Categorical distribution | 67 |

Binomial distribution | 68 |

Poisson distribution | 69 |

Multinomial distribution | 70 |

Pareto distribution and power law distribution | 71 |

Triangular distribution | 73 |

Normal distribution also known as the Gaussian distribution | 74 |

Normality tests | 77 |

Nonparametric continuous distributions | 78 |

Lognormal distribution | 79 |

Thin tails | 80 |

Joint normal distribution | 81 |

Beta distribution | 82 |

Auditing the design of business prediction models | 83 |

Process also known as a system | 84 |

Mathematical model | 85 |

Mixing models and registers | 86 |

Best guess forecasts | 97 |

Propagating uncertainty | 98 |

The flaw of averages | 99 |

Random | 100 |

Theoretically random | 101 |

Real life random | 102 |

Fooled by randomness 2 | 104 |

Monte Carlo simulation | 105 |

Ignoring real options | 109 |

Guessing impact | 111 |

Conditional dependence and independence | 112 |

Correlation also known as linear correlation | 113 |

Resampling | 114 |

Regression | 115 |

Dynamic models | 116 |

Auditing model fitting and validation | 117 |

Exhaustive mutually exclusive hypotheses | 118 |

Probabilities applied to alternative hypotheses | 119 |

Combining evidence | 120 |

Bayess theorem | 121 |

Model fitting | 123 |

Hyperparameters | 126 |

Bayesian model averaging | 128 |

Hypothesis testing | 129 |

Hypothesis testing in business | 130 |

Maximum a posteriori estimation MAP | 131 |

Median a posteriori estimation | 132 |

Best estimates of parameters | 135 |

Sampling distribution | 138 |

Robust estimators | 140 |

Data mining | 141 |

Searching for significance | 142 |

Exploratory data analysis | 143 |

Silly extrapolation | 144 |

Cross validation | 145 |

Happy history | 147 |

Information graphics | 148 |

Causation | 149 |

Auditing and samples | 151 |

Sample | 152 |

Sampling frame | 153 |

Probability sample also known as a random sample | 154 |

Equal probability sampling also known as simple random sampling | 155 |

Systematic sampling | 156 |

Sequential sampling | 157 |

Prejudging sample sizes | 158 |

Dropouts | 159 |

Small populations | 160 |

Auditing in the world of high finance | 163 |

Extreme values | 164 |

Stress testing | 165 |

Portfolio models | 166 |

Historical simulation | 168 |

Heteroskedasticity | 169 |

Parametric portfolio model | 170 |

Risk and reward | 171 |

Portfolio effect | 172 |

BlackScholes | 173 |

The Greeks | 175 |

### Other editions - View all

A Pocket Guide to Risk Mathematics: Key Concepts Every Auditor Should Know Matthew Leitch No preview available - 2010 |