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.