| Preface | p. vii |
| List of Symbols | p. ix |
| Modeling uncertain outcomes | p. 1 |
| The three M's of decision making under uncertainty | p. 1 |
| Probability models and scenario distributions | p. 4 |
| Distribution functions and quantile functions | p. 6 |
| Joint distributions and couplings | p. 8 |
| Utility functions and order relations | p. 12 |
| Compounding | p. 20 |
| Standard statistical parameters | p. 21 |
| Location parameters | p. 21 |
| Dispersion parameters | p. 22 |
| Correlation parameters | p. 24 |
| Measuring single-period risk | p. 27 |
| Probability functionals and their properties | p. 27 |
| Properties of probability functionals | p. 29 |
| Version-independent properties of probability functionals | p. 31 |
| Acceptability functionals and deviation risk functionals | p. 35 |
| Acceptance sets for translation-equivariant functionals | p. 39 |
| Dual representations of concave and convex functionals | p. 41 |
| The average value-at-risk | p. 48 |
| Kusuoka representations | p. 58 |
| Conditional acceptability and risk mappings | p. 66 |
| Version independent conditional acceptability mappings | p. 73 |
| More about the conditional average value-at-risk | p. 75 |
| Classes of version-independent acceptability-type functionals | p. 77 |
| Expected utility | p. 78 |
| Distortion functionals | p. 80 |
| Sup-convolutions | p. 88 |
| Single-period polyhedral acceptability functionals | p. 91 |
| Risk-corrected expectation and mean-risk models | p. 93 |
| Classes of version-independent deviation-type functionals | p. 94 |
| Deviation functionals of the form E[h(Y - EY)] | p. 95 |
| Deviation functionals of the form Y - EY [subscript h] | p. 99 |
| Deviation functionals of the form [Y - EY superscript -] [subscript h] | p. 102 |
| Deviation functionals of the form E[h(Y - Y[prime])] | p. 106 |
| Minimal loss risk functionals | p. 107 |
| Summary | p. 112 |
| Measuring multi-period risk | p. 115 |
| Introduction to multi-period models | p. 115 |
| Evolving information: filtrations and tree processes | p. 119 |
| Dynamic acceptability functionals | p. 124 |
| Introducing information into single-period functionals | p. 126 |
| Multi-period risk functionals: basic properties | p. 132 |
| Dual representations of multi-period acceptability functionals | p. 136 |
| Version-independent multi-period risk functionals | p. 140 |
| Classes of multi-period acceptability functionals | p. 144 |
| Separable functionals | p. 144 |
| Risk functionals of the value-of-information type | p. 146 |
| More about the multi-period average value-at-risk | p. 150 |
| Composition of conditional acceptability mappings | p. 154 |
| Polyhedral multi-period acceptability functionals | p. 159 |
| Polyhedral acceptability functionals in multi-stage stochastic programs | p. 169 |
| Summary | p. 172 |
| Single-stage decision models | p. 175 |
| Stochastic optimization | p. 175 |
| Efficient frontiers | p. 179 |
| Simple deviation risk models | p. 183 |
| Discrete models | p. 187 |
| Standard deviation efficiency | p. 188 |
| Lower standard deviation efficiency | p. 196 |
| Mean absolute deviation efficiency | p. 198 |
| Average value-at-risk deviation efficiency | p. 198 |
| Value-at-risk deviation efficiency | p. 200 |
| Minimal loss efficiency | p. 201 |
| Distortion efficiency | p. 202 |
| Risk contributions | p. 205 |
| Multi-stage decision models for financial management | p. 211 |
| Multi-stage decisions | p. 211 |
| Tree models | p. 216 |
| A typical multi-stage financial optimization problem | p. 217 |
| Value-of-information: standard and clairvoyant problems | p. 221 |
| Acceptability and value-of-information processes | p. 223 |
| An example for a value-of-information process | p. 224 |
| Efficient frontiers in multi-stage portfolio optimization | p. 229 |
| A multi-stage insurance model | p. 233 |
| Multi-stage decision models for electricity management | p. 245 |
| Introduction | p. 245 |
| Case study: Mean-risk portfolio optimization of a municipal power utility | p. 247 |
| Optimization model | p. 251 |
| Objective and multi-period polyhedral acceptability functionals | p. 258 |
| Simulation results | p. 260 |
| Conclusions | p. 263 |
| Probability spaces, [sigma]-fields and L[subscript p]-spaces | p. 265 |
| Fenchel-Moreau duality | p. 269 |
| Description of the data set used in Chapters 4 and 5 | p. 273 |
| Bibliography | p. 277 |
| Index | p. 285 |
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