A Pocket Guide to Risk Mathematics: Key Concepts Every Auditor Should Know

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John Wiley & Sons, Sep 7, 2010 - Business & Economics - 202 pages
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This 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."
Dr Sarah Blackburn, President at the Institute of Internal Auditors - UK and Ireland

 

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Contents

Contents start here
1
This book
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
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