Modeling, measuring and managing risk:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2007
|
| Subjects: | |
| Online Access: | Table of contents only Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke Includes bibliographical references (p. 277-284) and index |
| Physical Description: | XV, 286 S. graph. Darst. 24 cm |
| ISBN: | 9789812707406 9812707409 |
Staff View
MARC
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| 100 | 1 | |a Pflug, Georg |d 1951- |e Verfasser |0 (DE-588)115267670 |4 aut | |
| 245 | 1 | 0 | |a Modeling, measuring and managing risk |c Georg Ch. Pflug ; Werner Römisch |
| 246 | 1 | 3 | |a Risk |
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2007 | |
| 300 | |a XV, 286 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 500 | |a Includes bibliographical references (p. 277-284) and index | ||
| 650 | 4 | |a Functionals |x Statistical methods | |
| 650 | 4 | |a Risk assessment |x Statistical methods | |
| 650 | 4 | |a Risk management |x Statistical methods | |
| 650 | 4 | |a Decision making |x Statistical methods | |
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Record in the Search Index
| _version_ | 1804137562745339904 |
|---|---|
| adam_text | Contents
Preface vii
List of Symbols ix
1. Modeling uncertain outcomes 1
1.1 The three M s of decision making under uncertainty ... 1
1.2 Probability models and scenario distributions....... 4
1.2.1 Distribution functions and quantile functions ... 6
1.2.2 Joint distributions and couplings.......... 8
1.2.3 Utility functions and order relations........ 12
1.2.4 Compounding.................... 20
1.3 Standard statistical parameters............... 21
1.3.1 Location parameters................. 21
1.3.2 Dispersion parameters................ 22
1.3.3 Correlation parameters............... 24
xi
xii Modeling, Measuring and Managing Risk
2. Measuring single-period risk 27
2.1 Probability functionals and their properties........ 27
2.1.1 Properties of probability functionals........ 29
2.1.2 Version-independent properties of probability
functionals...................... 31
2.2 Acceptability functionals and deviation risk functionals . 35
2.2.1 Acceptance sets for translation-equivariant func-
tionals ........................ 39
2.2.2 Dual representations of concave and convex func-
tionals ........................ 41
2.2.3 The average value-at-risk.............. 48
2.2.4 Kusuoka representations .............. 58
2.3 Conditional acceptability and risk mappings........ 66
2.3.1 Version independent conditional acceptability
mappings....................... 73
2.3.2 More about the conditional average value-at-risk . 75
2.4 Classes of version-independent acceptability-type functionals 77
2.4.1 Expected utility................... 78
2.4.2 Distortion functionals ............... 80
2.4.3 Sup-convolutions................... 88
2.4.4 Single-period polyhedral acceptability functionals 91
2.4.5 Risk-corrected expectation and mean-risk models 93
2.5 Classes of version-independent deviation-type functionals 94
2.5.1 Deviation functionals of the form E[h(Y - EY)} . 95
2.5.2 Deviation functionals of the form Y - EY h . . 99
2.5.3 Deviation functionals of the form || [y-Ey] ||h 102
2.5.4 Deviation functionals of the form E[h(Y - Y )) . 106
2.5.5 Minimal loss risk functionals............ 107
2.6 Summary........................... 112
Contents xiii
3. Measuring multi-period risk 115
3.1 Introduction to multi-period models............ 115
3.1.1 Evolving information: nitrations and tree pro-
cesses ........................ 119
3.1.2 Dynamic acceptability functionals......... 124
3.1.3 Introducing information into single-period func-
tionals ........................ 126
3.2 Multi-period risk functionals: basic properties ...... 132
3.2.1 Dual representations of multi-period acceptability
functionals...................... 136
3.2.2 Version-independent multi-period risk functionals 140
3.3 Classes of multi-period acceptability functionals...... 144
3.3.1 Separable functionals................ 144
3.3.2 Risk functionals of the value-of-information type . 146
3.3.3 More about the multi-period average value-at-risk 150
3.3.4 Composition of conditional acceptability mappings 154
3.3.5 Polyhedral multi-period acceptability functionals . 159
3.3.6 Polyhedral acceptability functionals in multi-stage
stochastic programs ................ 169
3.4 Summary........................... 172
4. Single-stage decision models 175
4.1 Stochastic optimization ................... 175
4.2 Efficient frontiers....................... 179
4.2.1 Simple deviation risk models............ 183
4.2.2 Discrete models................... 187
4.2.3 Standard deviation efficiency ........... 188
xiv Modeling, Measuring and Managing Risk
4.2.4 Lower standard deviation efficiency........ 196
4.2.5 Mean absolute deviation efficiency ........ 198
4.2.6 Average value-at-risk deviation efficiency..... 198
4.2.7 Value-at-risk deviation efficiency ......... 200
4.2.8 Minimal loss efficiency ............... 201
4.2.9 Distortion efficiency................. 202
4.3 Risk contributions...................... 205
5. Multi-stage decision models for financial management 211
5.1 Multi-stage decisions..................... 211
5.1.1 Tree models..................... 216
5.1.2 A typical multi-stage financial optimization
problem........................ 217
5.2 Value-of-information: standard and clairvoyant problems . 221
5.2.1 Acceptability and value-of-information processes . 223
5.2.2 An example for a value-of-information process . . 224
5.3 Efficient frontiers in multi-stage portfolio optimization . . 229
5.4 A multi-stage insurance model ............... 233
6. Multi-stage decision models for electricity management 245
6.1 Introduction.......................... 245
6.2 Case study: Mean-risk portfolio optimization of a munici-
pal power utility....................... 247
6.2.1 Optimization model................. 251
6.2.2 Objective and multi-period polyhedral acceptabil-
ity functionals.................... 258
6.2.3 Simulation results.................. 260
6.3 Conclusions.......................... 263
Contents xv
Appendix A. Probability spaces, a-fields and Lp-spaces 265
Appendix B. Fenchel-Moreau duality 269
Appendix C. Description of the data set used in Chapters 4 and 5 273
Bibliography 277
Index 285
|
| adam_txt |
Contents
Preface vii
List of Symbols ix
1. Modeling uncertain outcomes 1
1.1 The three M's of decision making under uncertainty . 1
1.2 Probability models and scenario distributions. 4
1.2.1 Distribution functions and quantile functions . 6
1.2.2 Joint distributions and couplings. 8
1.2.3 Utility functions and order relations. 12
1.2.4 Compounding. 20
1.3 Standard statistical parameters. 21
1.3.1 Location parameters. 21
1.3.2 Dispersion parameters. 22
1.3.3 Correlation parameters. 24
xi
xii Modeling, Measuring and Managing Risk
2. Measuring single-period risk 27
2.1 Probability functionals and their properties. 27
2.1.1 Properties of probability functionals. 29
2.1.2 Version-independent properties of probability
functionals. 31
2.2 Acceptability functionals and deviation risk functionals . 35
2.2.1 Acceptance sets for translation-equivariant func-
tionals . 39
2.2.2 Dual representations of concave and convex func-
tionals . 41
2.2.3 The average value-at-risk. 48
2.2.4 Kusuoka representations . 58
2.3 Conditional acceptability and risk mappings. 66
2.3.1 Version independent conditional acceptability
mappings. 73
2.3.2 More about the conditional average value-at-risk . 75
2.4 Classes of version-independent acceptability-type functionals 77
2.4.1 Expected utility. 78
2.4.2 Distortion functionals . 80
2.4.3 Sup-convolutions. 88
2.4.4 Single-period polyhedral acceptability functionals 91
2.4.5 Risk-corrected expectation and mean-risk models 93
2.5 Classes of version-independent deviation-type functionals 94
2.5.1 Deviation functionals of the form E[h(Y - EY)} . 95
2.5.2 Deviation functionals of the form \\Y - EY\\h . . 99
2.5.3 Deviation functionals of the form || [y-Ey]"||h 102
2.5.4 Deviation functionals of the form E[h(Y - Y')) . 106
2.5.5 Minimal loss risk functionals. 107
2.6 Summary. 112
Contents xiii
3. Measuring multi-period risk 115
3.1 Introduction to multi-period models. 115
3.1.1 Evolving information: nitrations and tree pro-
cesses . 119
3.1.2 Dynamic acceptability functionals. 124
3.1.3 Introducing information into single-period func-
tionals . 126
3.2 Multi-period risk functionals: basic properties . 132
3.2.1 Dual representations of multi-period acceptability
functionals. 136
3.2.2 Version-independent multi-period risk functionals 140
3.3 Classes of multi-period acceptability functionals. 144
3.3.1 Separable functionals. 144
3.3.2 Risk functionals of the value-of-information type . 146
3.3.3 More about the multi-period average value-at-risk 150
3.3.4 Composition of conditional acceptability mappings 154
3.3.5 Polyhedral multi-period acceptability functionals . 159
3.3.6 Polyhedral acceptability functionals in multi-stage
stochastic programs . 169
3.4 Summary. 172
4. Single-stage decision models 175
4.1 Stochastic optimization . 175
4.2 Efficient frontiers. 179
4.2.1 Simple deviation risk models. 183
4.2.2 Discrete models. 187
4.2.3 Standard deviation efficiency . 188
xiv Modeling, Measuring and Managing Risk
4.2.4 Lower standard deviation efficiency. 196
4.2.5 Mean absolute deviation efficiency . 198
4.2.6 Average value-at-risk deviation efficiency. 198
4.2.7 Value-at-risk deviation efficiency . 200
4.2.8 Minimal loss efficiency . 201
4.2.9 Distortion efficiency. 202
4.3 Risk contributions. 205
5. Multi-stage decision models for financial management 211
5.1 Multi-stage decisions. 211
5.1.1 Tree models. 216
5.1.2 A typical multi-stage financial optimization
problem. 217
5.2 Value-of-information: standard and clairvoyant problems . 221
5.2.1 Acceptability and value-of-information processes . 223
5.2.2 An example for a value-of-information process . . 224
5.3 Efficient frontiers in multi-stage portfolio optimization . . 229
5.4 A multi-stage insurance model . 233
6. Multi-stage decision models for electricity management 245
6.1 Introduction. 245
6.2 Case study: Mean-risk portfolio optimization of a munici-
pal power utility. 247
6.2.1 Optimization model. 251
6.2.2 Objective and multi-period polyhedral acceptabil-
ity functionals. 258
6.2.3 Simulation results. 260
6.3 Conclusions. 263
Contents xv
Appendix A. Probability spaces, a-fields and Lp-spaces 265
Appendix B. Fenchel-Moreau duality 269
Appendix C. Description of the data set used in Chapters 4 and 5 273
Bibliography 277
Index 285 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Pflug, Georg 1951- Römisch, Werner 1975- |
| author_GND | (DE-588)115267670 (DE-588)131460293 |
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| author_role | aut aut |
| author_sort | Pflug, Georg 1951- |
| author_variant | g p gp w r wr |
| building | Verbundindex |
| bvnumber | BV023256677 |
| callnumber-first | Q - Science |
| callnumber-label | QA273 |
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| callnumber-sort | QA 3273.6 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 237 SK 850 |
| classification_tum | MAT 902f MAT 624f |
| ctrlnum | (OCoLC)134992753 (DE-599)BVBBV023256677 |
| dewey-full | 658.4/033 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 658 - General management |
| dewey-raw | 658.4/033 |
| dewey-search | 658.4/033 |
| dewey-sort | 3658.4 233 |
| dewey-tens | 650 - Management and auxiliary services |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV023256677 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:30:05Z |
| indexdate | 2024-07-09T21:14:16Z |
| institution | BVB |
| isbn | 9789812707406 9812707409 |
| language | English |
| lccn | 2007021405 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016441941 |
| oclc_num | 134992753 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-11 DE-188 DE-384 DE-29T DE-634 DE-19 DE-BY-UBM DE-521 |
| owner_facet | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-11 DE-188 DE-384 DE-29T DE-634 DE-19 DE-BY-UBM DE-521 |
| physical | XV, 286 S. graph. Darst. 24 cm |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Pflug, Georg 1951- Verfasser (DE-588)115267670 aut Modeling, measuring and managing risk Georg Ch. Pflug ; Werner Römisch Risk New Jersey [u.a.] World Scientific 2007 XV, 286 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Includes bibliographical references (p. 277-284) and index Functionals Statistical methods Risk assessment Statistical methods Risk management Statistical methods Decision making Statistical methods Entscheidung bei Risiko (DE-588)4225781-5 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Risikoanalyse (DE-588)4137042-9 gnd rswk-swf Risikofunktion (DE-588)4304955-2 gnd rswk-swf Risikomaß (DE-588)4716345-8 gnd rswk-swf Entscheidung bei Unsicherheit (DE-588)4070864-0 gnd rswk-swf Entscheidungsmodell (DE-588)4121201-0 gnd rswk-swf Risikomaß (DE-588)4716345-8 s Entscheidung bei Risiko (DE-588)4225781-5 s Stochastisches Modell (DE-588)4057633-4 s DE-604 Entscheidung bei Unsicherheit (DE-588)4070864-0 s Risikoanalyse (DE-588)4137042-9 s Risikofunktion (DE-588)4304955-2 s Entscheidungsmodell (DE-588)4121201-0 s DE-188 Römisch, Werner 1975- Verfasser (DE-588)131460293 aut http://www.loc.gov/catdir/toc/ecip0718/2007021405.html Table of contents only HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016441941&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pflug, Georg 1951- Römisch, Werner 1975- Modeling, measuring and managing risk Functionals Statistical methods Risk assessment Statistical methods Risk management Statistical methods Decision making Statistical methods Entscheidung bei Risiko (DE-588)4225781-5 gnd Stochastisches Modell (DE-588)4057633-4 gnd Risikoanalyse (DE-588)4137042-9 gnd Risikofunktion (DE-588)4304955-2 gnd Risikomaß (DE-588)4716345-8 gnd Entscheidung bei Unsicherheit (DE-588)4070864-0 gnd Entscheidungsmodell (DE-588)4121201-0 gnd |
| subject_GND | (DE-588)4225781-5 (DE-588)4057633-4 (DE-588)4137042-9 (DE-588)4304955-2 (DE-588)4716345-8 (DE-588)4070864-0 (DE-588)4121201-0 |
| title | Modeling, measuring and managing risk |
| title_alt | Risk |
| title_auth | Modeling, measuring and managing risk |
| title_exact_search | Modeling, measuring and managing risk |
| title_exact_search_txtP | Modeling, measuring and managing risk |
| title_full | Modeling, measuring and managing risk Georg Ch. Pflug ; Werner Römisch |
| title_fullStr | Modeling, measuring and managing risk Georg Ch. Pflug ; Werner Römisch |
| title_full_unstemmed | Modeling, measuring and managing risk Georg Ch. Pflug ; Werner Römisch |
| title_short | Modeling, measuring and managing risk |
| title_sort | modeling measuring and managing risk |
| topic | Functionals Statistical methods Risk assessment Statistical methods Risk management Statistical methods Decision making Statistical methods Entscheidung bei Risiko (DE-588)4225781-5 gnd Stochastisches Modell (DE-588)4057633-4 gnd Risikoanalyse (DE-588)4137042-9 gnd Risikofunktion (DE-588)4304955-2 gnd Risikomaß (DE-588)4716345-8 gnd Entscheidung bei Unsicherheit (DE-588)4070864-0 gnd Entscheidungsmodell (DE-588)4121201-0 gnd |
| topic_facet | Functionals Statistical methods Risk assessment Statistical methods Risk management Statistical methods Decision making Statistical methods Entscheidung bei Risiko Stochastisches Modell Risikoanalyse Risikofunktion Risikomaß Entscheidung bei Unsicherheit Entscheidungsmodell |
| url | http://www.loc.gov/catdir/toc/ecip0718/2007021405.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016441941&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT pfluggeorg modelingmeasuringandmanagingrisk AT romischwerner modelingmeasuringandmanagingrisk AT pfluggeorg risk AT romischwerner risk |