Intro -- Contents -- Preface -- List of Symbols -- 1. Modeling uncertain outcomes -- 1.1 The three M's of decision making under uncertainty -- 1.2 Probability models and scenario distributions -- 1.2.1 Distribution functions and quantile functions -- 1.2.2 Joint distributions and couplings -- 1.2.3 Utility functions and order relations -- 1.2.4 Compounding -- 1.3 Standard statistical parameters -- 1.3.1 Location parameters -- 1.3.2 Dispersion parameters -- 1.3.3 Correlation parameters -- 2. Measuring single-period risk -- 2.1 Probability functionals and their properties -- 2.1.1 Properties of probability functionals -- 2.1.2 Version-independent properties of probability functionals -- 2.2 Acceptability functionals and deviation risk functionals -- 2.2.1 Acceptance sets for translation-equivariant functionals -- 2.2.2 Dual representations of concave and convex functionals -- 2.2.3 The average value-at-risk -- 2.2.4 Kusuoka representations -- 2.3 Conditional acceptability and risk mappings -- 2.3.1 Version independent conditional acceptability mappings -- 2.3.2 More about the conditional average value-at-risk -- 2.4 Classes of version-independent acceptability-type functionals -- 2.4.1 Expected utility -- 2.4.2 Distortion functionals -- 2.4.3 Sup-convolutions -- 2.4.4 Single-period polyhedral acceptability functionals -- 2.4.5 Risk-corrected expectation and mean-risk models -- 2.5 Classes of version-independent deviation-type functionals -- 2.5.1 Deviation functionals of the form E[h(Y ¡ EY )] -- 2.5.2 Deviation functionals of the form ||Y - EY||h -- 2.5.3 Deviation functionals of the form ||[Y - EY ]-||h -- 2.5.4 Deviation functionals of the form E[h(Y - Y')] -- 2.5.5 Minimal loss risk functionals -- 2.6 Summary -- 3. Measuring multi-period risk -- 3.1 Introduction to multi-period models.

3.1.1 Evolving information: filtrations and tree pro- cesses -- 3.1.2 Dynamic acceptability functionals -- 3.1.3 Introducing information into single-period functionals -- 3.1.3.1 Expected conditional acceptability functionals -- 3.1.3.2 Dual extension of single-period functionals -- 3.2 Multi-period risk functionals: basic properties -- 3.2.1 Dual representations of multi-period acceptability functionals -- 3.2.2 Version-independent multi-period risk functionals -- 3.3 Classes of multi-period acceptability functionals -- 3.3.1 Separable functionals -- 3.3.2 Risk functionals of the value-of-information type -- 3.3.3 More about the multi-period average value-at-risk -- 3.3.4 Composition of conditional acceptability mappings -- 3.3.5 Polyhedral multi-period acceptability functionals -- 3.3.6 Polyhedral acceptability functionals in multi-stage stochastic programs -- 3.4 Summary -- 4. Single-stage decision models -- 4.1 Stochastic optimization -- 4.2 Effecient frontiers -- 4.2.1 Simple deviation risk models -- 4.2.2 Discrete models -- 4.2.3 Standard deviation efficiency -- 4.2.3.1 Introducing a risk-free asset -- 4.2.4 Lower standard deviation efficiency -- 4.2.5 Mean absolute deviation efficiency -- 4.2.6 Average value-at-risk deviation efficiency -- 4.2.7 Value-at-risk deviation efficiency -- 4.2.8 Minimal loss efficiency -- 4.2.9 Distortion efficiency -- 4.3 Risk contributions -- 5. Multi-stage decision models for financial management -- 5.1 Multi-stage decisions -- 5.1.1 Tree models -- 5.1.2 A typical multi-stage financial optimization problem -- 5.2 Value-of-information: standard and clairvoyant problems -- 5.2.1 Acceptability and value-of-information processes -- 5.2.2 An example for a value-of-information process -- 5.3 Efficient frontiers in multi-stage portfolio optimization -- 5.4 A multi-stage insurance model.

6. Multi-stage decision models for electricity management -- 6.1 Introduction -- 6.2 Case study: Mean-risk portfolio optimization of a municipal power utility -- 6.2.1 Optimization model -- 6.2.2 Objective and multi-period polyhedral acceptability functionals -- 6.2.3 Simulation results -- 6.3 Conclusions -- Appendix A. Probability spaces, fields and Lp-spaces -- Appendix B. Fenchel-Moreau duality -- Appendix C. Description of the data set used in Chapters 4 and 5 -- Bibliography -- Index.

Key Features:First comprehensive treatment of risk measures for single- and multi-period modelsIncludes applications in finance and electricityContains many illustrative examples, figures and graphical representations.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.