Introduction xiii

1 Foundations 1

Risk management: principles and practice 1

Definitions 3

Systematic and unsystematic risk 4

Insurable risks 4

Exposure 7

Management 7

Risk management 7

Risk management objectives 8

Organizational objectives 8

Other significant objectives 10

Risk management decision process 11

Step 1–Diagnosis of exposures 11

Step 2–Risk treatment 16

Step 3–Audit and corrective actions 19

State of the art and the trends in risk management 20

Risk profile, risk map or risk matrix 20

Frequency × Severity 20

Risk financing and strategic financing 23

From risk management to strategic risk management 23

From managing physical assets to managing reputation 25

From risk manager to chief risk officer 26

Why is risk quantification needed? 27

Risk quantification – a knowledge-based approach 28

Introduction 28

Causal structure of risk 28

Building a quantitative causal model of risk 31

Exposure, frequency, and probability 33

Exposure, occurrence, and impact drivers 34

Controlling exposure, occurrence, and impact 35

Controllable, predictable, observable, and hidden drivers 35

Cost of decisions 36

Risk financing 37

Risk management programme as an influence diagram 38

Modelling an individual risk or the risk management programme 39

Summary 41

2 Tool Box 43

Probability basics 43

Introduction to probability theory 43

Conditional probabilities 45

Independence 49

Bayes’ theorem 50

Random variables 54

Moments of a random variable 57

Continuous random variables 58

Main probability distributions 62

Introduction–the binomial distribution 62

Overview of usual distributions 64

Fundamental theorems of probability theory 67

Empirical estimation 68

Estimating probabilities from data 68

Fitting a distribution from data 69

Expert estimation 71

From data to knowledge 71

Estimating probabilities from expert knowledge 73

Estimating a distribution from expert knowledge 74

Identifying the causal structure of a domain 74

Conclusion 75

Bayesian networks and influence diagrams 76

Introduction to the case 77

Introduction to Bayesian networks 78

Nodes and variables 79

Probabilities 79

Dependencies 81

Inference 83

Learning 85

Extension to influence diagrams 87

Introduction to Monte Carlo simulation 90

Introduction 90

Introductory example: structured funds 90

Risk management example 1 – hedging weather risk 96

Description 96

Collecting information 98

Model 99

Manual scenario 101

Monte Carlo simulation 101

Summary 104

Risk management example 2– potential earthquake in cement industry 104

Analysis 104

Model 106

Monte Carlo simulation 107

Conclusion 109

A bit of theory 109

Introduction 109

Definition 110

Estimation according to Monte Carlo simulation 111

Random variable generation 112

Variance reduction 113

Software tools 117

3 Quantitative Risk Assessment: A Knowledge Modelling Process 119

Introduction 119

Increasing awareness of exposures and stakes 119

Objectives of risk assessment 120

Issues in risk quantification 121

Risk quantification: a knowledge management process 122

The basel II framework for operational risk 122

Introduction 123

The three pillars 123

Operational risk 124

The basic indicator approach 124

The sound practices paper 125

The standardized approach 125

The alternative standardized approach 127

The advanced measurement approaches (AMA) 127

Risk mitigation 130

Partial use 130

Conclusion 131

Identification and mapping of loss exposures 131

Quantification of loss exposures 134

The candidate scenarios for quantitative risk assessment 134

The exposure, occurrence, impact (XOI) model 135

Modelling and conditioning exposure at peril 135

Summary 136

Modelling and conditioning occurrence 137

Consistency of exposure and occurrence 137

Evaluating the probability of occurrence 140

Conditioning the probability of occurrence 143

Summary 144

Modelling and conditioning impact 145

Defining the impact equation 145

Defining the distributions of variables involved 146

Identifying drivers 147

Summary 148

Quantifying a single scenario 148

An example – “fat fingers” scenario 150

Modelling the exposure 150

Modelling the occurrence 151

Modelling the impact 152

Quantitative simulation 154

Merging scenarios 157

Modelling the global distribution of losses 158

Conclusion 159

4 Identifying Risk Control Drivers 161

Introduction 161

Loss control – a qualitative view 163

Loss prevention (action on the causes) 164

Eliminating the exposure 164

Reducing the probability of occurrence 166

Loss reduction (action on the consequences) 166

Pre-event or passive reduction 166

Post-event or active reduction 167

An introduction to cindynics 169

Basic concepts 170

Dysfunctions 172

General principles and axioms 174

Perspectives 174

Quantitative example 1 – pandemic influenza 176

Introduction 176

The influenza pandemic risk model 177

Exposure 177

Occurrence 177

Impact 178

The Bayesian network 180

Risk control 181

Pre-exposition treatment (vaccination) 182

Post-exposition treatment (antiviral drug) 182

Implementation within a Bayesian network 183

Strategy comparison 185

Cumulated point of view 185

Discussion 188

Quantitative example 2 – basel II operational risk 189

The individual loss model 189

Analysing the potential severe losses 189

Identifying the loss control actions 189

Analysing the cumulated impact of loss control actions 191

Discussion 192

Quantitative example 3 – enterprise-wide risk management 194

Context and objectives 195

Risk analysis and complex systems 195

An alternative definition of risk 196

Representation using Bayesian networks 196

Selection of a time horizon 197

Identification of objectives 197

Identification of risks (events) and risk factors (context) 198

Structuring the network 199

Identification of relationships (causal links or influences) 200

Quantification of the network 200

Example of global enterprise risk representation 200

Usage of the model for loss control 201

Risk mapping 201

Importance factors 202

Scenario analysis 202

Application to the risk management of an industrial plant 203

Description of the system 203

Assessment of the external risks 204

Integration of external risks in the global risk assessment 207

Usage of the model for risk management 210

Summary – using quantitative models for risk control 210

5 Risk Financing: The Right Cost of Risks 211

Introduction 211

Risk financing instruments 212

Retention techniques 214

Current treatment 214

Reserves 215

Captives (insurance or reinsurance) 215

Transfer techniques 219

Contractual transfer (for risk financing – to a noninsurer) 219

Purchase of insurance cover 219

Hybrid techniques 220

Pools and closed mutual 220

Claims history-based premiums 222

Choice of retention levels 222

Financial reinsurance and finite risks 223

Prospective aggregate cover 225

Capital markets products for risk financing 225

Securitization 226

Insurance derivatives 227

Contingent capital arrangements 228

Risk financing and risk quantifying 230

Using quantitative models 231

Example 1: Satellite launcher 231

Example 2: Defining a property insurance programme 243

A tentative general representation of financing methods 252

Introduction 252

Risk financing building blocks 254

Usual financing tools revisited 257

Combining a risk model and a financing model 261

Conclusion 263

Index 267