Preface xiii

1 What is risk management? 1

1.1 Introduction 2

1.2 Identifying and documenting risk 5

1.3 Fallacies and traps in risk management 7

1.4 Why safety is different 9

1.5 The Basel framework 11

1.6 Hold or hedge? 12

1.7 Learning from a disaster 13

Notes 17

References 18

Exercises 19

2 The structure of risk 22

2.1 Introduction to probability and risk 23

2.2 The structure of risk 25

2.3 Portfolios and diversification 30

2.4 The impact of correlation 40

2.5 Using copulas to model multivariate distributions 49

Notes 58

References 59

Exercises 60

3 Measuring risk 63

3.1 How can we measure risk? 64

3.2 Value at risk 67

3.3 Combining and comparing risks 73

3.4 VaR in practice 76

3.5 Criticisms of VaR 79

3.6 Beyond value at risk 82

Notes 88

References 88

Exercises 89

4 Understanding the tails 92

4.1 Heavy-tailed distributions 93

4.2 Limiting distributions for the maximum 100

4.3 Excess distributions 109

4.4 Estimation using extreme value theory 115

Notes 121

References 122

Exercises 123

5 Making decisions under uncertainty 125

5.1 Decisions, states and outcomes 126

5.2 Expected Utility Theory 130

5.3 Stochastic dominance and risk profiles 148

5.4 Risk decisions for managers 156

Notes 160

References 161

Exercises 162

6 Understanding risk behavior 164

6.1 Why decision theory fails 165

6.2 Prospect Theory 172

6.3 Cumulative Prospect Theory 180

6.4 Decisions with ambiguity 189

6.5 How managers treat risk 191

Notes 194

References 194

Exercises 195

7 Stochastic optimization 198

7.1 Introduction to stochastic optimization 199

7.2 Choosing scenarios 212

7.3 Multistage stochastic optimization 218

7.4 Value at risk constraints 224

Notes 228

References 228

Exercises 229

8 Robust optimization 232

8.1 True uncertainty: Beyond probabilities 233

8.2 Avoiding disaster when there is uncertainty 234

8.3 Robust optimization and the minimax approach 250

Notes 261

References 262

Exercises 263

9 Real options 265

9.1 Introduction to real options 266

9.2 Calculating values with real options 267

9.3 Combining real options and net present value 273

9.4 The connection with financial options 278

9.5 Using Monte Carlo simulation to value real options 282

9.6 Some potential problems with the use of real options 285

Notes 287

References 287

Exercises 288

10 Credit risk 291

10.1 Introduction to credit risk 292

10.2 Using credit scores for credit risk 294

10.3 Consumer credit 301

10.4 Logistic regression 308

Notes 317

References 318

Exercises 319

Appendix A Tutorial on probability theory 323

A.1 Random events 323

A.2 Bayes' rule and independence 326

A.3 Random variables 327

A.4 Means and variances 329

A.5 Combinations of random variables 332

A.6 The normal distribution and the Central Limit Theorem 336

Appendix B Answers to even-numbered exercises 340

Index 361