Risk Quantification

LAURENT CONDAMIN is engineer of the French Grande Ecole “Ecole Centrale de Paris”, PhD in Applied Mathematics and Associate in Risk Management (Insurance Institute of America). He is currently partner and managing director of Elseware where he makes consultancy on risk modelling in top leading companies. JEAN-PAUL LOUISOT is a civil engineer, Master in Economics, Master in Business Administration (Kellog, 1972) and Associate in Risk Management. He has spent more than thirty years of his career to service private and public entities helping them manage their risks and coach their risk managers and executives. As director for the CARM_institute, Ltd, he is in charge of the professional designations ARM and EFARM. As a Professor at Panthéon/Sorbonne University, he teaches a postgraduate course in Risk Management. Jean-Paul teaches also in various Engineering Schools and MBA programs. Previous publications include Exposure Diagnostic (AFNOR – 2004) and 100 Questions to understand Risk Management (AFNOR – 2005).PATRICK NAIM graduated from Ecole Centrale de Paris, and Associate in Risk Management (ARM). He is the founder and CEO of Elseware, a consulting company specialising in quantitative modelling and risk quantification. He also teaches data modelling and Bayesian Networks in several universities and engineering schools in France. He is author of several books in the field of quantitative modelling.

• Foreword xiIntroduction xiii1 Foundations 1Risk management: principles and practice 1Definitions 3Systematic and unsystematic risk 4Insurable risks 4Exposure 7Management 7Risk management 7Risk management objectives 8Organizational objectives 8Other significant objectives 10Risk management decision process 11Step 1–Diagnosis of exposures 11Step 2–Risk treatment 16Step 3–Audit and corrective actions 19State of the art and the trends in risk management 20Risk profile, risk map or risk matrix 20Frequency × Severity 20Risk financing and strategic financing 23From risk management to strategic risk management 23From managing physical assets to managing reputation 25From risk manager to chief risk officer 26Why is risk quantification needed? 27Risk quantification – a knowledge-based approach 28Introduction 28Causal structure of risk 28Building a quantitative causal model of risk 31Exposure, frequency, and probability 33Exposure, occurrence, and impact drivers 34Controlling exposure, occurrence, and impact 35Controllable, predictable, observable, and hidden drivers 35Cost of decisions 36Risk financing 37Risk management programme as an influence diagram 38Modelling an individual risk or the risk management programme 39Summary 412 Tool Box 43Probability basics 43Introduction to probability theory 43Conditional probabilities 45Independence 49Bayes’ theorem 50Random variables 54Moments of a random variable 57Continuous random variables 58Main probability distributions 62Introduction–the binomial distribution 62Overview of usual distributions 64Fundamental theorems of probability theory 67Empirical estimation 68Estimating probabilities from data 68Fitting a distribution from data 69Expert estimation 71From data to knowledge 71Estimating probabilities from expert knowledge 73Estimating a distribution from expert knowledge 74Identifying the causal structure of a domain 74Conclusion 75Bayesian networks and influence diagrams 76Introduction to the case 77Introduction to Bayesian networks 78Nodes and variables 79Probabilities 79Dependencies 81Inference 83Learning 85Extension to influence diagrams 87Introduction to Monte Carlo simulation 90Introduction 90Introductory example: structured funds 90Risk management example 1 – hedging weather risk 96Description 96Collecting information 98Model 99Manual scenario 101Monte Carlo simulation 101Summary 104Risk management example 2– potential earthquake in cement industry 104Analysis 104Model 106Monte Carlo simulation 107Conclusion 109A bit of theory 109Introduction 109Definition 110Estimation according to Monte Carlo simulation 111Random variable generation 112Variance reduction 113Software tools 1173 Quantitative Risk Assessment: A Knowledge Modelling Process 119Introduction 119Increasing awareness of exposures and stakes 119Objectives of risk assessment 120Issues in risk quantification 121Risk quantification: a knowledge management process 122The basel II framework for operational risk 122Introduction 123The three pillars 123Operational risk 124The basic indicator approach 124The sound practices paper 125The standardized approach 125The alternative standardized approach 127The advanced measurement approaches (AMA) 127Risk mitigation 130Partial use 130Conclusion 131Identification and mapping of loss exposures 131Quantification of loss exposures 134The candidate scenarios for quantitative risk assessment 134The exposure, occurrence, impact (XOI) model 135Modelling and conditioning exposure at peril 135Summary 136Modelling and conditioning occurrence 137Consistency of exposure and occurrence 137Evaluating the probability of occurrence 140Conditioning the probability of occurrence 143Summary 144Modelling and conditioning impact 145Defining the impact equation 145Defining the distributions of variables involved 146Identifying drivers 147Summary 148Quantifying a single scenario 148An example – “fat fingers” scenario 150Modelling the exposure 150Modelling the occurrence 151Modelling the impact 152Quantitative simulation 154Merging scenarios 157Modelling the global distribution of losses 158Conclusion 1594 Identifying Risk Control Drivers 161Introduction 161Loss control – a qualitative view 163Loss prevention (action on the causes) 164Eliminating the exposure 164Reducing the probability of occurrence 166Loss reduction (action on the consequences) 166Pre-event or passive reduction 166Post-event or active reduction 167An introduction to cindynics 169Basic concepts 170Dysfunctions 172General principles and axioms 174Perspectives 174Quantitative example 1 – pandemic influenza 176Introduction 176The influenza pandemic risk model 177Exposure 177Occurrence 177Impact 178The Bayesian network 180Risk control 181Pre-exposition treatment (vaccination) 182Post-exposition treatment (antiviral drug) 182Implementation within a Bayesian network 183Strategy comparison 185Cumulated point of view 185Discussion 188Quantitative example 2 – basel II operational risk 189The individual loss model 189Analysing the potential severe losses 189Identifying the loss control actions 189Analysing the cumulated impact of loss control actions 191Discussion 192Quantitative example 3 – enterprise-wide risk management 194Context and objectives 195Risk analysis and complex systems 195An alternative definition of risk 196Representation using Bayesian networks 196Selection of a time horizon 197Identification of objectives 197Identification of risks (events) and risk factors (context) 198Structuring the network 199Identification of relationships (causal links or influences) 200Quantification of the network 200Example of global enterprise risk representation 200Usage of the model for loss control 201Risk mapping 201Importance factors 202Scenario analysis 202Application to the risk management of an industrial plant 203Description of the system 203Assessment of the external risks 204Integration of external risks in the global risk assessment 207Usage of the model for risk management 210Summary – using quantitative models for risk control 2105 Risk Financing: The Right Cost of Risks 211Introduction 211Risk financing instruments 212Retention techniques 214Current treatment 214Reserves 215Captives (insurance or reinsurance) 215Transfer techniques 219Contractual transfer (for risk financing – to a noninsurer) 219Purchase of insurance cover 219Hybrid techniques 220Pools and closed mutual 220Claims history-based premiums 222Choice of retention levels 222Financial reinsurance and finite risks 223Prospective aggregate cover 225Capital markets products for risk financing 225Securitization 226Insurance derivatives 227Contingent capital arrangements 228Risk financing and risk quantifying 230Using quantitative models 231Example 1: Satellite launcher 231Example 2: Defining a property insurance programme 243A tentative general representation of financing methods 252Introduction 252Risk financing building blocks 254Usual financing tools revisited 257Combining a risk model and a financing model 261Conclusion 263Index 267