Risk Analysis: A Quantitative Guide

TLDR: In this article, the authors present a risk analysis approach based on Monte-Carlo simulation, which is used to fit a first-order parametric distribution to observed data and then combine it with a second-order probability distribution.

Abstract: Preface. Part 1: Introduction. 1. Why do a risk analysis? 1.1. Moving on from "What If" Scenarios. 1.2. The Risk Analysis Process. 1.3. Risk Management Options. 1.4. Evaluating Risk Management Options. 1.5. Inefficiencies in Transferring Risks to Others. 1.6. Risk Registers. 2. Planning a risk analysis. 2.1. Questions and Motives. 2.2. Determine the Assumptions that are Acceptable or Required. 2.3. Time and Timing. 2.4. You'll Need a Good Risk Analyst or Team. 3. The quality of a risk analysis. 3.1. The Reasons Why a Risk Analysis can be Terrible. 3.2. Communicating the Quality of Data Used in a Risk Analysis. 3.3. Level of Criticality. 3.4. The Biggest Uncertainty in a Risk Analysis. 3.5. Iterate. 4. Choice of model structure. 4.1. Software Tools and the Models they Build. 4.2. Calculation Methods. 4.3. Uncertainty and Variability. 4.4. How Monte Carlo Simulation Works. 4.5. Simulation Modelling. 5. Understanding and using the results of a risk analysis. 5.1. Writing a Risk Analysis Report. 5.2. Explaining a Model's Assumptions. 5.3. Graphical Presentation of a Model's Results. 5.4. Statistical Methods of Analysing Results. Part 2: Introduction. 6. Probability mathematics and simulation. 6.1. Probability Distribution Equations. 6.2. The Definition of "Probability". 6.3. Probability Rules. 6.4. Statistical Measures. 7. Building and running a model. 7.1. Model Design and Scope. 7.2. Building Models that are Easy to Check and Modify. 7.3. Building Models that are Efficient. 7.4. Most Common Modelling Errors. 8. Some basic random processes. 8.1. Introduction. 8.2. The Binomial Process. 8.3. The Poisson Process. 8.4. The Hypergeometric Process. 8.5. Central Limit Theorem. 8.6. Renewal Processes. 8.7. Mixture Distributions. 8.8. Martingales. 8.9. Miscellaneous Example. 9. Data and statistics. 9.1. Classical Statistics. 9.2. Bayesian Inference. 9.3. The Bootstrap. 9.4. Maximum Entropy Principle. 9.5. Which Technique Should You Use? 9.6. Adding uncertainty in Simple Linear Least-Squares Regression Analysis. 10. Fitting distributions to data. 10.1. Analysing the Properties of the Observed Data. 10.2. Fitting a Non-Parametric Distribution to the Observed Data. 10.3. Fitting a First-Order Parametric Distribution to Observed Data. 10.4. Fitting a Second-Order Parametric Distribution to Observed Data. 11. Sums of random variables. 11.1. The Basic Problem. 11.2. Aggregate Distributions. 12. Forecasting with uncertainty. 12.1. The Properties of a Time Series Forecast. 12.2. Common Financial Time Series Models. 12.3. Autoregressive Models. 12.4. Markov Chain Models. 12.5. Birth and Death Models. 12.6. Time Series Projection of Events Occurring Randomly in Time. 12.7. Time Series Models with Leading Indicators. 12.8. Comparing Forecasting Fits for Different Models. 12.9. Long-Term Forecasting. 13. Modelling correlation and dependencies. 13.1. Introduction. 13.2. Rank Order Correlation. 13.3. Copulas. 13.4. The Envelope Method. 13.5. Multiple Correlation Using a Look-Up Table. 14. Eliciting from expert opinion. 14.1. Introduction. 14.2. Sources of Error in Subjective Estimation. 14.3. Modelling Techniques. 14.4. Calibrating Subject Matter Experts. 14.5. Conducting a Brainstorming Session. 14.6. Conducting the Interview. 15. Testing and modelling causal relationships. 15.1. Campylobacter Example. 15.2. Types of Model to Analyse Data. 15.3. From Risk Factors to Causes. 15.4. Evaluating Evidence. 15.5. The Limits of Causal Arguments. 15.6. An Example of a Qualitative Causal Analysis. 15.7. Is Causal Analysis Essential? 16. Optimisation in risk analysis. 16.1. Introduction. 16.2. Optimisation Methods. 16.3. Risk Analysis Modelling and Optimisation. 16.4. Working Example: Optimal Allocation of Mineral Pots. 17. Checking and validating a model. 17.1. Spreadsheet Model Errors. 17.2. Checking Model Behaviour. 17.3. Comparing Predictions Against Reality. 18. Discounted cashflow modelling. 18.1. Useful Time Series Models of Sales and Market Size. 18.2. Summing Random Variables. 18.3. Summing Variable Margins on Variable Revenues. 18.4. Financial Measures in Risk Analysis. 19. Project risk analysis. 19.1. Cost Risk Analysis. 19.2. Schedule Risk Analysis. 19.3. Portfolios of risks. 19.4. Cascading Risks. 20. Insurance and finance risk analysis modelling. 20.1. Operational Risk Modelling. 20.2. Credit Risk. 20.3. Credit Ratings and Markov Chain Models. 20.4. Other Areas of Financial Risk. 20.5. Measures of Risk. 20.6. Term Life Insurance. 20.7. Accident Insurance. 20.8. Modelling a Correlated Insurance Portfolio. 20.9. Modelling Extremes. 20.10. Premium Calculations. 21. Microbial food safety risk assessment. 21.1. Growth and Attenuation Models. 21.2. Dose-Response Models. 21.3. Is Monte Carlo Simulation the Right Approach? 21.4. Some Model Simplifications. 22. Animal import risk assessment. 22.1. Testing for an Infected Animal. 22.2. Estimating True Prevalence in a Population. 22.3. Importing Problems. 22.4. Confidence of Detecting an Infected Group. 22.5. Miscellaneous Animal Health and Food Safety Problems. I. Guide for lecturers. II. About ModelRisk. III. A compendium of distributions. III.1. Discrete and Continuous Distributions. III.2. Bounded and Unbounded Distributions. III.3. Parametric and Non-Parametric Distributions. III.4. Univariate and Multivariate Distributions. III.5. Lists of Applications and the Most Useful Distributions. III.6. How to Read Probability Distribution Equations. III.7. The Distributions. III.8. Introduction to Creating Your Own Distributions. III.9. Approximation of One Distribution with Another. III.10. Recursive Formulae for Discrete Distributions. III.11. A Visual Observation On The Behaviour Of Distributions. IV. Further reading. V. Vose Consulting. References. Index.