Risk management and risk measurement: a geometric approach to risk space analysis
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
1999
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 252 S. graph. Darst. |
Internformat
MARC
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| 100 | 1 | |a Gaese, Ralf |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Risk management and risk measurement |b a geometric approach to risk space analysis |c vorgelegt von Ralf Gaese |
| 264 | 1 | |c 1999 | |
| 300 | |a XVI, 252 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 502 | |a St. Gallen, Univ., Diss., 1998 | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | Overview of Contents
1 Introduction 1
1.1 Motivation 1
1.2 Outline 7
2 Risk Management 11
2.1 Risk 11
2.2 Regulation 16
2.3 Failures 33
3 Risk Measurement 47
3.1 Abstraction 48
3.2 Measures 59
3.3 Risk ranking 78
3.4 Methods 94
3.5 Conclusions 99
4 Risk Space Geometry 105
4.1 Convex bodies 107
4.2 Spherical bodies 119
4.3 Subdivision 142
4.4 Conclusions 159
5 Risk Space Analysis 165
5.1 Approximation 166
5.2 Association 183
5.3 Refinement 195
5.4 Conclusions 208
A Mathematics Compendium 219
Contents
Preface v
Overview of Contents vii
Contents ix
List of Figures xiii
List of Definitions xv
1 Introduction 1
1.1 Motivation 1
1.2 Outline 7
2 Risk Management 11
2.1 Risk 11
2.1.1 Types 11
2.1.1.1 Financial risk 12
2.1.1.2 Market risk 14
2.1.2 Management 14
2.2 Regulation 16
2.2.1 Global Derivatives Study Group 16
2.2.1.1 Derivatives: Practices and Principles 17
2.2.2 Basle Committee on Banking Supervision 19
2.2.2.1 Capital adequacy 19
2.2.2.2 Internal models 25
2.2.2.3 Backtesting 29
2.3 Failures 33
x Contents
2.3.1 Metallgesellschaft 34
2.3.2 Orange County 41
3 Risk Measurement 47
3.1 Abstraction 48
3.1.1 Risk 48
3.1.2 Ambiguity 51
3.1.3 Aggregation 53
3.1.4 Coherency 55
3.2 Measures 59
3.2.1 Sensitivities 59
3.2.1.1 Duration measures 60
3.2.1.2 Greek letters 64
3.2.2 Maximum loss 67
3.2.3 Moments 68
3.2.3.1 Mean, variance Co 69
3.2.3.2 Lower partial moments 72
3.2.3.3 Distribution function 74
3.2.4 Quantiles 75
3.2.4.1 Quantile function 75
3.2.4.2 Value at risk 76
3.2.4.3 Generalized value at risk 78
3.3 Risk ranking 78
3.3.1 Stochastic dominance 80
3.3.2 Expected utility theory 84
3.3.3 Compatibility 90
3.4 Methods 94
3.4.1 Analytical solutions 94
3.4.1.1 Linear profiles 94
3.4.1.2 Quadratic profiles 96
3.4.2 Simulation 98
3.4.2.1 Historical simulation 98
3.4.2.2 Monte Carlo simulation 98
3.5 Conclusions 99
3.5.1 In summary 99
3.5.2 Issues 101
Contents xi
4 Risk Space Geometry 105
4.1 Convex bodies 107
4.1.1 Simplices 107
4.1.1.1 Regular simplices 110
4.1.2 Duplices 114
4.1.2.1 Normal duplices 118
4.1.2.2 Unbounded duplices 118
4.2 Spherical bodies 119
4.2.1 Balls and spheres 120
4.2.1.1 Ellipsoids 122
4.2.2 Spherical simplices 126
4.2.2.1 Normal spherical simplices 131
4.2.3 Spherical duplices 133
4.2.3.1 Normal spherical duplices 137
4.2.3.2 Unbounded spherical duplices 137
4.2.4 Ballooned simplices 138
4.3 Subdivision 142
4.3.1 Subdivision and refinement 142
4.3.2 Local subdivision 146
4.3.2.1 Convex simplices 146
4.3.2.2 Convex duplices 149
4.3.2.3 Spherical bodies 151
4.3.3 Global subdivision 153
4.4 Conclusions 159
4.4.1 In summary 160
4.4.2 Issues 163
5 Risk Space Analysis 165
5.1 Approximation 166
5.1.1 Decomposition 166
5.1.2 Approximation by discretization 168
5.1.2.1 Monopolistic approach 168
5.1.2.2 Oligopolistic approach 169
5.1.2.3 Polypolistic approach 170
5.1.3 Barycentric discretization 171
5.1.3.1 Inner barycentric approximation 173
5.1.3.2 Outer barycentric approximation 174
5.1.3.3 Alternative barycentric discretizations 175
5.1.4 Approximation without discretization 176
xij Contents
5.1.5 Compactness 181
5.2 Association 183
5.2.1 Taylor polynomials 183
5.2.1.1 Global Taylor approximation 184
5.2.1.2 Local Taylor approximation 186
5.2.2 Tailored functions 187
5.2.2.1 Convex simplices 187
5.2.2.2 Convex duplices 189
5.2.2.3 Spherical simplices 191
5.2.2.4 Spherical duplices 194
5.2.2.5 Ballooned simplices 195
5.3 Refinement 195
5.3.1 Dynamic subdivision 196
5.3.1.1 Subdivision characteristics 196
5.3.1.2 Refinement objectives 201
5.3.1.3 Refinement strategies 203
5.4 Conclusions 208
5.4.1 In summary 209
5.4.2 Instances 213
5.4.3 Issues 217
A Mathematics Compendium 219
A.I Spaces 219
A.2 Measure theory 221
A.3 Probability theory 224
A.4 Integration theory 227
A.4.1 Riemann integration 227
A.4.2 Riemann Stieltjes integration 228
A.4.3 Lebesgue integration 229
A.4.4 Expectation 232
A.5 Varia 234
Abbreviations and Acronyms 235
Notation 237
Bibliography 243
List of Figures
1 1 Value at risk the classic illustration 2
1 2 Subdivision into convex simplices 3
1 3 Inner and outer barycentric discretization 4
1 4 Subdivision into spherical duplices 6
3 1 Distribution function and quantile function 76
3 2 Incompatibility of VaR with second degree stochastic dominance 93
4 1 Construction of a regular triangle by transformation 113
4 2 Convex 2 duplices: degenerate, non degenerate, and normal . . 115
4 3 Transformation of the unit circle into an ellipse 124
4 4 Blowing up of a triangle to an ellipse 128
4 5 Spherical 2 simplices: degenerate, non degenerate, and normal. 130
4 6 Spherical 2 duplices: degenerate, non degenerate, and normal . 134
4 7 First attempt at blowing up 140
4 8 Second attempt at blowing up 141
4 9 Ballooned simplices 142
4 10 Subdivision of a 3 duplex into three tetrahedra 151
4 11 Subdivision of a spherical 2 simplex into six subsimplices . . . 159
5 1 Continuous approach applied to a spherical duplex 179
5 2 Synopsis of approximation approaches 210
5 3 Prototypes of approximation methods 215
List of Definitions
3 1 Risk situation 48
3 2 Risk evolvement 49
3 3 Risk measure 50
3 4 Ambiguous risk situation 51
3 5 Ambiguous risk evolvement 51
3 6 Risk measure, ambiguous case 52
3 7 Coherency 56
3 8 Risk order 79
4 1 Convex duplex 114
4 2 Unbounded convex duplex 118
4 3 Blowing up 128
4 4 Spherical simplex 129
4 5 Spherical duplex 134
4 6 Unbounded spherical duplex 137
4 7 Ballooned simplex 141
4 8 Subdivision 142
4 9 Refinement 144
4 10 Complete subdivision 145
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| indexdate | 2024-07-09T18:30:40Z |
| institution | BVB |
| language | English |
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| spelling | Gaese, Ralf Verfasser aut Risk management and risk measurement a geometric approach to risk space analysis vorgelegt von Ralf Gaese 1999 XVI, 252 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier St. Gallen, Univ., Diss., 1998 Wahrscheinlichkeitsraum (DE-588)4410515-0 gnd rswk-swf Messung (DE-588)4038852-9 gnd rswk-swf Risikomanagement (DE-588)4121590-4 gnd rswk-swf Risiko (DE-588)4050129-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Risikomanagement (DE-588)4121590-4 s Risiko (DE-588)4050129-2 s Messung (DE-588)4038852-9 s Wahrscheinlichkeitsraum (DE-588)4410515-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008568978&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gaese, Ralf Risk management and risk measurement a geometric approach to risk space analysis Wahrscheinlichkeitsraum (DE-588)4410515-0 gnd Messung (DE-588)4038852-9 gnd Risikomanagement (DE-588)4121590-4 gnd Risiko (DE-588)4050129-2 gnd |
| subject_GND | (DE-588)4410515-0 (DE-588)4038852-9 (DE-588)4121590-4 (DE-588)4050129-2 (DE-588)4113937-9 |
| title | Risk management and risk measurement a geometric approach to risk space analysis |
| title_auth | Risk management and risk measurement a geometric approach to risk space analysis |
| title_exact_search | Risk management and risk measurement a geometric approach to risk space analysis |
| title_full | Risk management and risk measurement a geometric approach to risk space analysis vorgelegt von Ralf Gaese |
| title_fullStr | Risk management and risk measurement a geometric approach to risk space analysis vorgelegt von Ralf Gaese |
| title_full_unstemmed | Risk management and risk measurement a geometric approach to risk space analysis vorgelegt von Ralf Gaese |
| title_short | Risk management and risk measurement |
| title_sort | risk management and risk measurement a geometric approach to risk space analysis |
| title_sub | a geometric approach to risk space analysis |
| topic | Wahrscheinlichkeitsraum (DE-588)4410515-0 gnd Messung (DE-588)4038852-9 gnd Risikomanagement (DE-588)4121590-4 gnd Risiko (DE-588)4050129-2 gnd |
| topic_facet | Wahrscheinlichkeitsraum Messung Risikomanagement Risiko Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008568978&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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