A probability metrics approach to financial risk measures:
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley-Blackwell
2011
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 375 graph. Darst. |
| ISBN: | 9781405183697 |
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MARC
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| 245 | 1 | 0 | |a A probability metrics approach to financial risk measures |c Svetlozar T. Rachev ; Stoyan V. Stoyanov ; Frank J. Fabozzi |
| 264 | 1 | |a Chichester [u.a.] |b Wiley-Blackwell |c 2011 | |
| 300 | |a XVI, 375 |b graph. Darst. | ||
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| 700 | 1 | |a Stoyanov, Stoyan Veselinov |e Verfasser |4 aut | |
| 700 | 1 | |a Fabozzi, Frank J. |d 1948- |e Verfasser |0 (DE-588)129772054 |4 aut | |
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Record in the Search Index
| _version_ | 1804143240377532416 |
|---|---|
| adam_text | Contents
Preface
xiii
About the Authors
xv
1
Introduction
1
1.1
Probability Metrics
1
1.2
Applications in Finance
2
2
Probability Distances and Metrics
7
2.1
Introduction
9
2.2
Some Examples of Probability Metrics
9
2.2.1
Engineer s metric
10
2.2.2
Uniform (or Kolmogorov) metric
10
2.2.3
Levy metric
11
2.2.4
Kantorovich metric
14
2.2.5
Lp-metrics between distribution functions
15
2.2.6
Ky Fan metrics
16
2.2.7
Lp-metric
17
2.3
Distance and Semidistance Spaces
19
2.4
Definitions of Probability Distances and Metrics
24
2.5
Summary
28
2.6
Technical Appendix
28
2.6.1
Universally measurable separable metric spaces
29
2.6.2
The equivalence of the notions of
p.
(semi-)distance
on
Т>г
and on X
35
vu
CONTENTS
Choice under Uncertainty
40
3.1
Introduction
41
3.2
Expected Utility Theory
44
3.2.1
St Petersburg Paradox
44
3.2.2
The
von Neumann-Morgenstern
expected
utility theory
46
3.2.3
Types of utility functions
48
3.3
Stochastic Dominance
51
3.3.1
First-order stochastic dominance
52
3.3.2
Second-order stochastic dominance
53
3.3.3
Rothschild-Stiglitz stochastic dominance
55
3.3.4
Third-order stochastic dominance
56
3.3.5
Efficient sets and the portfolio choice problem
58
3.3.6
Return versus payoff
59
3.4
Probability Metrics and Stochastic Dominance
63
3.5
Cumulative Prospect Theory
66
3.6
Summary
70
3.7
Technical Appendix
70
3.7.1
The axioms of choice
71
3.7.2
Stochastic dominance relations of order
η
72
3.7.3
Return versus payoff and stochastic dominance
74
3.7.4
Other stochastic dominance relations
76
A Classification of Probability Distances
83
4.1
Introduction
86
4.2
Primary Distances and Primary Metrics
86
4.3
Simple Distances and Metrics
90
4.4
Compound Distances and Moment Functions
99
4.5
Ideal Probability Metrics
105
4.5.1
Interpretation and examples of ideal probability
metrics
107
4.5.2
Conditions for boundedness of ideal probability
metrics
112
4.6
Summary
114
4.7
Technical Appendix
114
4.7.1
Examples of primary distances
114
4.7.2
Examples of simple distances
118
4.7.3
Examples of compound distances
131
4.7.4
Examples of moment functions
135
viii
CONTENTS
Risk and Uncertainty
146
5.1
Introduction
147
5.2
Measures of Dispersion
150
5.2.1
Standard deviation
151
5.2.2
Mean absolute deviation
153
5.2.3
Semi-standard deviation
154
5.2.4
Axiomatic description
155
5.2.5
Deviation measures
156
5.3
Probability Metrics and Dispersion Measures
158
5.4
Measures of Risk
159
5.4.1
Value-at-risk
160
5.4.2
Computing portfolio VaR in practice
165
5.4.3
Back-testing of VaR
172
5.4.4
Coherent risk measures
175
5.5
Risk Measures and Dispersion Measures
179
5.6
Risk Measures and Stochastic Orders
181
5.7
Summary
182
5.8
Technical Appendix
183
5.8.1
Convex risk measures
183
5.8.2
Probability metrics and deviation measures
184
5.8.3
Deviation measures and probability
quasi-metrics
187
Average Value-at-Risk
191
6.1
Introduction
192
6.2
Average Value-at-Risk
193
6.2.1
AVaR for stable distributions
200
6.3
AVaR Estimation from a Sample
204
6.4
Computing Portfolio AVaR in Practice
207
6.4.1
The multivariate normal assumption
207
6.4.2
The historical method
208
6.4.3
The hybrid method
208
6.4.4
The Monte Carlo method
209
6.4.5
Kernel methods
211
6.5
Back-testing of AVaR
218
6.6
Spectral Risk Measures
220
6.7
Risk Measures and Probability Metrics
223
6.8
Risk Measures Based on Distortion Functionals
226
6.9
Summary
227
ix
CONTENTS
6.10 Technical Appendix 228
6.10.1 Characteristics
of conditional loss distributions
228
6.10.2
Higher-order AVaR
232
6.10.3
The minimization formula for AVaR
234
6.10.4
ETLvsAVaR
237
6.10.5
Kernel-based estimation of AVaR
242
6.10.6
Remarks on spectral risk measures
245
Computing AVaR through Monte Carlo
252
7.1
Introduction
253
7.2
An Illustration of Monte Carlo Variability
256
7.3
Asymptotic Distribution, Classical Conditions
259
7.4
Rate of Convergence to the Normal Distribution
262
7.4.1
The effect of tail thickness
263
7.4.2
The effect of tail truncation
268
7.4.3
Infinite variance distributions
271
7.5
Asymptotic Distribution, Heavy-tailed Returns
277
7.6
Rate of Convergence, Heavy-tailed Returns
283
7.6.1
Stable
Paretian
distributions
283
7.6.2
Student s
t
distribution
286
7.7
On the Choice of a Distributional Model
290
7.7.1
Tail behavior and return frequency
290
7.7.2
Practical implications
295
7.8
Summary
297
7.9
Technical Appendix
298
7.9.1
Proof of the stable limit result
298
Stochastic Dominance Revisited
304
8.1
Introduction
306
8.2
Metrization of Preference Relations
308
8.3
The Hausdorff Metric Structure
310
8.4
Examples
314
8.4.1
The Levy quasi-semidistance and first-order
stochastic dominance
315
8.4.2
Higher-order stochastic dominance
317
8.4.3
The H-quasi-semidistance
320
8.4.4
AVaR generated stochastic orders
322
8.4.5
Compound quasi-semidistances
324
8.5
Utility-type Representations
325
CONTENTS
8.6
Almost Stochastic Orders and Degree of Violation
328
8.7
Summary
330
8.8
Technical Appendix
332
8.8.1
Preference relations and topology
332
8.8.2
Quasi-semidistances and preference relations
334
8.8.3
Construction of quasi-semidistances on classes
of investors
335
8.8.4
Investors with balanced views
338
8.8.5
Structural classification of probability distances
339
Index
357
Xl
|
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| author_GND | (DE-588)12022979X (DE-588)129772054 |
| author_facet | Račev, Svetlozar T. 1951- Stoyanov, Stoyan Veselinov Fabozzi, Frank J. 1948- |
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| author_sort | Račev, Svetlozar T. 1951- |
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| bvnumber | BV036627842 |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| indexdate | 2024-07-09T22:44:31Z |
| institution | BVB |
| isbn | 9781405183697 |
| language | English |
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| spelling | Račev, Svetlozar T. 1951- Verfasser (DE-588)12022979X aut A probability metrics approach to financial risk measures Svetlozar T. Rachev ; Stoyan V. Stoyanov ; Frank J. Fabozzi Chichester [u.a.] Wiley-Blackwell 2011 XVI, 375 graph. Darst. txt rdacontent n rdamedia nc rdacarrier Portfolio Selection (DE-588)4046834-3 gnd rswk-swf Risiko (DE-588)4050129-2 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Messung (DE-588)4038852-9 gnd rswk-swf Portfolio Selection (DE-588)4046834-3 s Risiko (DE-588)4050129-2 s Messung (DE-588)4038852-9 s Finanzmathematik (DE-588)4017195-4 s b DE-604 Stoyanov, Stoyan Veselinov Verfasser aut Fabozzi, Frank J. 1948- Verfasser (DE-588)129772054 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020547727&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Račev, Svetlozar T. 1951- Stoyanov, Stoyan Veselinov Fabozzi, Frank J. 1948- A probability metrics approach to financial risk measures Portfolio Selection (DE-588)4046834-3 gnd Risiko (DE-588)4050129-2 gnd Finanzmathematik (DE-588)4017195-4 gnd Messung (DE-588)4038852-9 gnd |
| subject_GND | (DE-588)4046834-3 (DE-588)4050129-2 (DE-588)4017195-4 (DE-588)4038852-9 |
| title | A probability metrics approach to financial risk measures |
| title_auth | A probability metrics approach to financial risk measures |
| title_exact_search | A probability metrics approach to financial risk measures |
| title_full | A probability metrics approach to financial risk measures Svetlozar T. Rachev ; Stoyan V. Stoyanov ; Frank J. Fabozzi |
| title_fullStr | A probability metrics approach to financial risk measures Svetlozar T. Rachev ; Stoyan V. Stoyanov ; Frank J. Fabozzi |
| title_full_unstemmed | A probability metrics approach to financial risk measures Svetlozar T. Rachev ; Stoyan V. Stoyanov ; Frank J. Fabozzi |
| title_short | A probability metrics approach to financial risk measures |
| title_sort | a probability metrics approach to financial risk measures |
| topic | Portfolio Selection (DE-588)4046834-3 gnd Risiko (DE-588)4050129-2 gnd Finanzmathematik (DE-588)4017195-4 gnd Messung (DE-588)4038852-9 gnd |
| topic_facet | Portfolio Selection Risiko Finanzmathematik Messung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020547727&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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