{"product_id":"a-pocket-guide-to-risk-mathematics-9780470710524","title":"A Pocket Guide to Risk Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis uniquely accessible, breakthrough book lets auditors grasp the thinking behind the mathematical approach to risk \u003ci\u003ewithout\u003c\/i\u003e doing the mathematics.  \u003cp\u003eRisk 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.\u003c\/p\u003e \u003cp\u003eSpend 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.\u003c\/p\u003e \u003cp\u003eI 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.\u003cbr\u003e \u003cb\u003eDr Sarah Blackburn\u003c\/b\u003e, President at the Institute of Internal Auditors - UK and Ireland\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eStart here 1\u003c\/p\u003e \u003cp\u003eGood choice! 1\u003c\/p\u003e \u003cp\u003eThis book 2\u003c\/p\u003e \u003cp\u003eHow this book works 3\u003c\/p\u003e \u003cp\u003eThe myth of mathematical clarity 5\u003c\/p\u003e \u003cp\u003eThe myths of quantification 7\u003c\/p\u003e \u003cp\u003eThe auditor’s mission 8\u003c\/p\u003e \u003cp\u003eAuditing simple risk assessments 11\u003c\/p\u003e \u003cp\u003e1 Probabilities 12\u003c\/p\u003e \u003cp\u003e2 Probabilistic forecaster 13\u003c\/p\u003e \u003cp\u003e3 Calibration (also known as reliability) 13\u003c\/p\u003e \u003cp\u003e4 Resolution 14\u003c\/p\u003e \u003cp\u003e5 Proper score function 15\u003c\/p\u003e \u003cp\u003e6 Audit point: Judging probabilities 17\u003c\/p\u003e \u003cp\u003e7 Probability interpretations 17\u003c\/p\u003e \u003cp\u003e8 Degree of belief 18\u003c\/p\u003e \u003cp\u003e9 Situation (also known as an experiment) 19\u003c\/p\u003e \u003cp\u003e10 Long run relative frequency 20\u003c\/p\u003e \u003cp\u003e11 Degree of belief about long run relative frequency 21\u003c\/p\u003e \u003cp\u003e12 Degree of belief about an outcome 22\u003c\/p\u003e \u003cp\u003e13 Audit point: Mismatched interpretations of probability 24\u003c\/p\u003e \u003cp\u003e14 Audit point: Ignoring uncertainty about probabilities 25\u003c\/p\u003e \u003cp\u003e15 Audit point: Not using data to illuminate probabilities 25\u003c\/p\u003e \u003cp\u003e16 Outcome space (also known as sample space, or possibility space) 26\u003c\/p\u003e \u003cp\u003e17 Audit point: Unspecified situations 27\u003c\/p\u003e \u003cp\u003e18 Outcomes represented without numbers 28\u003c\/p\u003e \u003cp\u003e19 Outcomes represented with numbers 29\u003c\/p\u003e \u003cp\u003e20 Random variable 29\u003c\/p\u003e \u003cp\u003e21 Event 30\u003c\/p\u003e \u003cp\u003e22 Audit point: Events with unspecified boundaries 31\u003c\/p\u003e \u003cp\u003e23 Audit point: Missing ranges 32\u003c\/p\u003e \u003cp\u003e24 Audit point: Top 10 risk reporting 32\u003c\/p\u003e \u003cp\u003e25 Probability of an outcome 33\u003c\/p\u003e \u003cp\u003e26 Probability of an event 34\u003c\/p\u003e \u003cp\u003e27 Probability measure (also known as probability distribution, probability function, or even probability distribution function) 34\u003c\/p\u003e \u003cp\u003e28 Conditional probabilities 36\u003c\/p\u003e \u003cp\u003e29 Discrete random variables 37\u003c\/p\u003e \u003cp\u003e30 Continuous random variables 38\u003c\/p\u003e \u003cp\u003e31 Mixed random variables (also known as mixed discrete-continuous random variables) 39\u003c\/p\u003e \u003cp\u003e32 Audit point: Ignoring mixed random variables 40\u003c\/p\u003e \u003cp\u003e33 Cumulative probability distribution function 41\u003c\/p\u003e \u003cp\u003e34 Audit point: Ignoring impact spread 43\u003c\/p\u003e \u003cp\u003e35 Audit point: Confusing money and utility 44\u003c\/p\u003e \u003cp\u003e36 Probability mass function 44\u003c\/p\u003e \u003cp\u003e37 Probability density function 45\u003c\/p\u003e \u003cp\u003e38 Sharpness 47\u003c\/p\u003e \u003cp\u003e39 Risk 49\u003c\/p\u003e \u003cp\u003e40 Mean value of a probability distribution (also known as the expected value) 50\u003c\/p\u003e \u003cp\u003e41 Audit point: Excessive focus on expected values 51\u003c\/p\u003e \u003cp\u003e42 Audit point: Misunderstanding ‘expected’ 51\u003c\/p\u003e \u003cp\u003e43 Audit point: Avoiding impossible provisions 52\u003c\/p\u003e \u003cp\u003e44 Audit point: Probability impact matrix numbers 53\u003c\/p\u003e \u003cp\u003e45 Variance 54\u003c\/p\u003e \u003cp\u003e46 Standard deviation 55\u003c\/p\u003e \u003cp\u003e47 Semi-variance 55\u003c\/p\u003e \u003cp\u003e48 Downside probability 55\u003c\/p\u003e \u003cp\u003e49 Lower partial moment 56\u003c\/p\u003e \u003cp\u003e50 Value at risk (VaR) 56\u003c\/p\u003e \u003cp\u003e51 Audit point: Probability times impact 58\u003c\/p\u003e \u003cp\u003eSome types of probability distribution 61\u003c\/p\u003e \u003cp\u003e52 Discrete uniform distribution 62\u003c\/p\u003e \u003cp\u003e53 Zipf distribution 62\u003c\/p\u003e \u003cp\u003e54 Audit point: Benford’s law 64\u003c\/p\u003e \u003cp\u003e55 Non-parametric distributions 65\u003c\/p\u003e \u003cp\u003e56 Analytical expression 65\u003c\/p\u003e \u003cp\u003e57 Closed form (also known as a closed formula or explicit formula) 66\u003c\/p\u003e \u003cp\u003e58 Categorical distribution 67\u003c\/p\u003e \u003cp\u003e59 Bernoulli distribution 67\u003c\/p\u003e \u003cp\u003e60 Binomial distribution 68\u003c\/p\u003e \u003cp\u003e61 Poisson distribution 69\u003c\/p\u003e \u003cp\u003e62 Multinomial distribution 70\u003c\/p\u003e \u003cp\u003e63 Continuous uniform distribution 70\u003c\/p\u003e \u003cp\u003e64 Pareto distribution and power law distribution 71\u003c\/p\u003e \u003cp\u003e65 Triangular distribution 73\u003c\/p\u003e \u003cp\u003e66 Normal distribution (also known as the Gaussian distribution) 74\u003c\/p\u003e \u003cp\u003e67 Audit point: Normality tests 77\u003c\/p\u003e \u003cp\u003e68 Non-parametric continuous distributions 78\u003c\/p\u003e \u003cp\u003e69 Audit point: Multi-modal distributions 78\u003c\/p\u003e \u003cp\u003e70 Lognormal distribution 79\u003c\/p\u003e \u003cp\u003e71 Audit point: Thin tails 80\u003c\/p\u003e \u003cp\u003e72 Joint distribution 80\u003c\/p\u003e \u003cp\u003e73 Joint normal distribution 81\u003c\/p\u003e \u003cp\u003e74 Beta distribution 82\u003c\/p\u003e \u003cp\u003eAuditing the design of business prediction models 83\u003c\/p\u003e \u003cp\u003e75 Process (also known as a system) 84\u003c\/p\u003e \u003cp\u003e76 Population 84\u003c\/p\u003e \u003cp\u003e77 Mathematical model 85\u003c\/p\u003e \u003cp\u003e78 Audit point: Mixing models and registers 86\u003c\/p\u003e \u003cp\u003e79 Probabilistic models (also known as stochastic models or statistical models) 86\u003c\/p\u003e \u003cp\u003e80 Model structure 88\u003c\/p\u003e \u003cp\u003e81 Audit point: Lost assumptions 89\u003c\/p\u003e \u003cp\u003e82 Prediction formulae 89\u003c\/p\u003e \u003cp\u003e83 Simulations 90\u003c\/p\u003e \u003cp\u003e84 Optimization 90\u003c\/p\u003e \u003cp\u003e85 Model inputs 90\u003c\/p\u003e \u003cp\u003e86 Prediction formula structure 91\u003c\/p\u003e \u003cp\u003e87 Numerical equation solving 93\u003c\/p\u003e \u003cp\u003e88 Prediction algorithm 94\u003c\/p\u003e \u003cp\u003e89 Prediction errors 94\u003c\/p\u003e \u003cp\u003e90 Model uncertainty 94\u003c\/p\u003e \u003cp\u003e91 Audit point: Ignoring model uncertainty 95\u003c\/p\u003e \u003cp\u003e92 Measurement uncertainty 96\u003c\/p\u003e \u003cp\u003e93 Audit point: Ignoring measurement uncertainty 96\u003c\/p\u003e \u003cp\u003e94 Audit point: Best guess forecasts 97\u003c\/p\u003e \u003cp\u003e95 Prediction intervals 97\u003c\/p\u003e \u003cp\u003e96 Propagating uncertainty 98\u003c\/p\u003e \u003cp\u003e97 Audit point: The flaw of averages 99\u003c\/p\u003e \u003cp\u003e98 Random 100\u003c\/p\u003e \u003cp\u003e99 Theoretically random 101\u003c\/p\u003e \u003cp\u003e100 Real life random 102\u003c\/p\u003e \u003cp\u003e101 Audit point: Fooled by randomness (1) 102\u003c\/p\u003e \u003cp\u003e102 Audit point: Fooled by randomness (2) 104\u003c\/p\u003e \u003cp\u003e103 Pseudo random number generation 104\u003c\/p\u003e \u003cp\u003e104 Monte Carlo simulation 105\u003c\/p\u003e \u003cp\u003e105 Audit point: Ignoring real options 109\u003c\/p\u003e \u003cp\u003e106 Tornado diagram 109\u003c\/p\u003e \u003cp\u003e107 Audit point: Guessing impact 111\u003c\/p\u003e \u003cp\u003e108 Conditional dependence and independence 112\u003c\/p\u003e \u003cp\u003e109 Correlation (also known as linear correlation) 113\u003c\/p\u003e \u003cp\u003e110 Copulas 113\u003c\/p\u003e \u003cp\u003e111 Resampling 114\u003c\/p\u003e \u003cp\u003e112 Causal modelling 114\u003c\/p\u003e \u003cp\u003e113 Latin hypercube 114\u003c\/p\u003e \u003cp\u003e114 Regression 115\u003c\/p\u003e \u003cp\u003e115 Dynamic models 116\u003c\/p\u003e \u003cp\u003e116 Moving average 116\u003c\/p\u003e \u003cp\u003eAuditing model fitting and validation 117\u003c\/p\u003e \u003cp\u003e117 Exhaustive, mutually exclusive hypotheses 118\u003c\/p\u003e \u003cp\u003e118 Probabilities applied to alternative hypotheses 119\u003c\/p\u003e \u003cp\u003e119 Combining evidence 120\u003c\/p\u003e \u003cp\u003e120 Prior probabilities 120\u003c\/p\u003e \u003cp\u003e121 Posterior probabilities 120\u003c\/p\u003e \u003cp\u003e122 Bayes’s theorem 121\u003c\/p\u003e \u003cp\u003e123 Model fitting 123\u003c\/p\u003e \u003cp\u003e124 Hyperparameters 126\u003c\/p\u003e \u003cp\u003e125 Conjugate distributions 126\u003c\/p\u003e \u003cp\u003e126 Bayesian model averaging 128\u003c\/p\u003e \u003cp\u003e127 Audit point: Best versus true explanation 128\u003c\/p\u003e \u003cp\u003e128 Hypothesis testing 129\u003c\/p\u003e \u003cp\u003e129 Audit point: Hypothesis testing in business 130\u003c\/p\u003e \u003cp\u003e130 Maximum a posteriori estimation (MAP) 131\u003c\/p\u003e \u003cp\u003e131 Mean a posteriori estimation 131\u003c\/p\u003e \u003cp\u003e132 Median a posteriori estimation 132\u003c\/p\u003e \u003cp\u003e133 Maximum likelihood estimation (MLE) 132\u003c\/p\u003e \u003cp\u003e134 Audit point: Best estimates of parameters 135\u003c\/p\u003e \u003cp\u003e135 Estimators 135\u003c\/p\u003e \u003cp\u003e136 Sampling distribution 138\u003c\/p\u003e \u003cp\u003e137 Least squares fitting 138\u003c\/p\u003e \u003cp\u003e138 Robust estimators 140\u003c\/p\u003e \u003cp\u003e139 Over-fitting 140\u003c\/p\u003e \u003cp\u003e140 Data mining 141\u003c\/p\u003e \u003cp\u003e141 Audit point: Searching for ‘significance’ 142\u003c\/p\u003e \u003cp\u003e142 Exploratory data analysis 143\u003c\/p\u003e \u003cp\u003e143 Confirmatory data analysis 143\u003c\/p\u003e \u003cp\u003e144 Interpolation and extrapolation 143\u003c\/p\u003e \u003cp\u003e145 Audit Point: Silly extrapolation 144\u003c\/p\u003e \u003cp\u003e146 Cross validation 145\u003c\/p\u003e \u003cp\u003e147 R2 (the coefficient of determination) 145\u003c\/p\u003e \u003cp\u003e148 Audit point: Happy history 147\u003c\/p\u003e \u003cp\u003e149 Audit point: Spurious regression results 147\u003c\/p\u003e \u003cp\u003e150 Information graphics 148\u003c\/p\u003e \u003cp\u003e151 Audit point: Definition of measurements 148\u003c\/p\u003e \u003cp\u003e152 Causation 149\u003c\/p\u003e \u003cp\u003eAuditing and samples 151\u003c\/p\u003e \u003cp\u003e153 Sample 152\u003c\/p\u003e \u003cp\u003e154 Audit point: Mixed populations 152\u003c\/p\u003e \u003cp\u003e155 Accessible population 152\u003c\/p\u003e \u003cp\u003e156 Sampling frame 153\u003c\/p\u003e \u003cp\u003e157 Sampling method 153\u003c\/p\u003e \u003cp\u003e158 Probability sample (also known as a random sample) 154\u003c\/p\u003e \u003cp\u003e159 Equal probability sampling (also known as simple random sampling) 155\u003c\/p\u003e \u003cp\u003e160 Stratified sampling 155\u003c\/p\u003e \u003cp\u003e161 Systematic sampling 156\u003c\/p\u003e \u003cp\u003e162 Probability proportional to size sampling 156\u003c\/p\u003e \u003cp\u003e163 Cluster sampling 156\u003c\/p\u003e \u003cp\u003e164 Sequential sampling 157\u003c\/p\u003e \u003cp\u003e165 Audit point: Prejudging sample sizes 158\u003c\/p\u003e \u003cp\u003e166 Dropouts 159\u003c\/p\u003e \u003cp\u003e167 Audit point: Small populations 160\u003c\/p\u003e \u003cp\u003eAuditing in the world of high finance 163\u003c\/p\u003e \u003cp\u003e168 Extreme values 164\u003c\/p\u003e \u003cp\u003e169 Stress testing 165\u003c\/p\u003e \u003cp\u003e170 Portfolio models 166\u003c\/p\u003e \u003cp\u003e171 Historical simulation 168\u003c\/p\u003e \u003cp\u003e172 Heteroskedasticity 169\u003c\/p\u003e \u003cp\u003e173 RiskMetrics variance model 169\u003c\/p\u003e \u003cp\u003e174 Parametric portfolio model 170\u003c\/p\u003e \u003cp\u003e175 Back-testing 170\u003c\/p\u003e \u003cp\u003e176 Audit point: Risk and reward 171\u003c\/p\u003e \u003cp\u003e177 Portfolio effect 172\u003c\/p\u003e \u003cp\u003e178 Hedge 172\u003c\/p\u003e \u003cp\u003e179 Black–Scholes 173\u003c\/p\u003e \u003cp\u003e180 The Greeks 175\u003c\/p\u003e \u003cp\u003e181 Loss distributions 176\u003c\/p\u003e \u003cp\u003e182 Audit point: Operational loss data 178\u003c\/p\u003e \u003cp\u003e183 Generalized linear models 179\u003c\/p\u003e \u003cp\u003eCongratulations 181\u003c\/p\u003e \u003cp\u003eUseful websites 183\u003c\/p\u003e \u003cp\u003eIndex 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