Mathematical risk analysis: dependence, risk bounds, optimal allocations and portfolios
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2013
|
| Schriftenreihe: | Springer series in operations research and financial engineering
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XII, 408 S. |
| ISBN: | 3642335896 9783642335891 |
Internformat
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Datensatz im Suchindex
| _version_ | 1807955001331417088 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
PART I STOCHASTIC DEPENDENCE AND EXTREMAL RISK
1 COPULAS, SKLAR'S THEOREM, AND DISTRIBUTIONAL TRANSFORM 3
1.1 SKLAR'S THEOREM AND THE DISTRIBUTIONAL TRANSFORM 3
1.2 COPULA MODELS AND COPULA CONSTRUCTIONS 7
1.2.1 SOME CLASSES OF COPULAS 8
1.2.2 COPULAS AND L 2 -PROJECTIONS 11
1.3 MULTIVARIATE DISTRIBUTIONAL AND QUANTILE TRANSFORM 14
1.4 PAIR COPULA CONSTRUCTION OF COPULA MODELS 17
1.5 APPLICATIONS OF THE DISTRIBUTIONAL TRANSFORM 21
1.5.1 APPLICATION TO STOCHASTIC ORDERING 21
1.5.2 OPTIMAL COUPLINGS 23
1.5.3 IDENTIFICATION AND GOODNESS OF FIT TESTS 25
1.5.4 EMPIRICAL COPULA PROCESS AND EMPIRICAL DEPENDENCE FUNCTION 26
1.6 MULTIVARIATE AND OVERLAPPING MARGINALS 28
1.6.1 GENERALIZED FRECHET CLASS 28
1.6.2 COPULAS WITH GIVEN INDEPENDENCE STRUCTURE 31
1.6.3 COPULAS, OVERLAPPING MARGINALS, AND L 2 -PROJECTIONS. 33
2 FRECHET CLASSES, RISK BOUNDS, AND DUALITY THEORY 35
2.1 DUAL REPRESENTATION OF GENERALIZED FRECHET BOUNDS 37
2.2 FRECHET BOUNDS COMONOTONICITY AND EXTREMAL RISK 45
3 CONVEX ORDER, EXCESS OF LOSS, AND COMONOTONICITY 53
3.1 CONVEX ORDER AND COMONOTONICITY 53
3.2 SCHUR ORDER AND REARRANGEMENTS 57
3.3 REARRANGEMENTS AND EXCESS OF LOSS 63
3.4 INTEGRAL ORDERS AND - .^-DIFFUSIONS 66
IX
HTTP://D-NB.INFO/1025398823
IMAGE 2
X
CONTENTS
4 BOUNDS FOR THE DISTRIBUTION FUNCTION AND VALUE AT RISK OF
THE JOINT PORTFOLIO 71
4.1 STANDARD BOUNDS 72
4.2 CONDITIONAL MOMENT METHOD 79
4.3 DUAL BOUNDS 82
5 RESTRICTIONS ON THE DEPENDENCE STRUCTURE 91
5.1 RESTRICTION TO POSITIVE DEPENDENT RISK VECTORS 91
5.2 HIGHER ORDER MARGINALS 95
5.2.1 A REDUCTION PRINCIPLE AND BONFERRONI TYPE BOUNDS 97 5.2.2 THE
CONDITIONING METHOD 103
5.2.3 REDUCTION BOUNDS FOR THE JOINT PORTFOLIO IN GENERAL MARGINAL
SYSTEMS 107
6 DEPENDENCE ORDERINGS OF RISK VECTORS AND PORTFOLIOS 113
6.1 POSITIVE ORTHANT DEPENDENCE AND SUPERMODULAR ORDERING 113 6.2
ASSOCIATION, CONDITIONAL INCREASING VECTORS, AND POSITIVE SUPERMODULAR
DEPENDENCE 120
6.3 DIRECTIONALLY CONVEX ORDER 124
6.3.1 BASIC PROPERTIES OF THE DIRECTIONALLY CONVEX ORDER 124 6.3.2
FURTHER CRITERIA FOR DCX 126
6.3.3 DIRECTIONALLY CONVEX ORDER IN FUNCTIONAL MODELS 128
6.4 DEPENDENCE ORDERINGS IN MODELS WITH MULTIVARIATE MARGINALS . 131
PART II RISK MEASURES AND WORST CASE
PORTFOLIOS
7 RISK MEASURES FOR REAL RISKS 141
7.1 SOME CLASSES OF RISK MEASURES FOR REAL VARIABLES 142
7.1.1 BASIC PROPERTIES OF RISK MEASURES 142
7.1.2 EXAMPLES OF RISK MEASURES 146
7.2 REPRESENTATION AND CONTINUITY PROPERTIES OF CONVEX RISK MEASURES ON
L P - SPACES 153
7.2.1 CONVEX DUALITY AND CONTINUITY RESULTS 154
7.2.2 REPRESENTATION OF COHERENT AND CONVEX RISK MEASURES ON L P 157
7.2.3 CONTINUITY RESULTS FOR RISK MEASURES ON L P 160
8 RISK MEASURES FOR PORTFOLIO VECTORS 167
8.1 BASIC PROPERTIES OF PORTFOLIO RISK MEASURES 168
8.2 CLASSES OF EXAMPLES OF PORTFOLIO RISK MEASURES 174
8.2.1 AGGREGATION TYPE RISK MEASURES 174
8.2.2 * MULTIVARIATE DISTORTION AND QUANTILE-TYPE RISK MEASURES 180
IMAGE 3
CONTENTS XI
8.3 REPRESENTATION AND CONTINUITY OF CONVEX RISK
MEASURES ON L P D 184
9 LAW INVARIANT CONVEX RISK MEASURES ON L P D AND OPTIMAL MASS
TRANSPORTATION 189
9.1 LAW INVARIANT RISK MEASURES AND OPTIMAL MASS TRANSPORTATION 190
9.2 MULTIVARIATE COMONOTONICITY AND THE ^-COUPLING PROBLEM 198 9.3 WORST
CASE PORTFOLIO VECTORS AND DIVERSIFICATION EFFECTS 207
9.4 EXAMPLES OF WORST CASE RISK PORTFOLIOS AND WORST CASE
DIVERSIFICATION EFFECTS 214
PART III OPTIMAL RISK ALLOCATION
10 OPTIMAL ALLOCATIONS AND PARETO EQUILIBRIUM 227
10.1 PARETO EQUILIBRIUM AND RELATED RISK MEASURES IN THE COHERENT CASE
227
10.2 OPTIMAL ALLOCATIONS UNDER ADMISSIBILITY RESTRICTIONS 235
10.3 PARETO EQUILIBRIUM FOR CONVEX RISK MEASURES 248
10.4 PARETO OPTIMALITY, COMONOTONICITY, AND EXISTENCE OF OPTIMAL
ALLOCATIONS 256
11 CHARACTERIZATION AND EXAMPLES OF OPTIMAL RISK ALLOCATIONS FOR CONVEX
RISK FUNCTIONALS 265
11.1 INF-CONVOLUTION AND CONVEX CONJUGATES 266
11.2 CHARACTERIZATION OF OPTIMAL ALLOCATIONS 269
11.3 EXAMPLES OF OPTIMAL RISK ALLOCATIONS 276
11.3.1 EXPECTED RISK FUNCTIONALS 277
11.3.2 DILATED RISK FUNCTIONALS 278
11.3.3 AVERAGE VALUE AT RISK AND STOP-LOSS CONTRACTS 279
11.3.4 MEAN VARIANCE VERSUS STANDARD DEVIATION RISK FUNCTIONALS 280
11.4 OPTIMAL ALLOCATION OF RISK VECTORS 283
11.4.1 CHARACTERIZATION OF OPTIMAL ALLOCATIONS 284
11.4.2 LAW INVARIANT RISK MEASURES AND COMONOTONICITY 289 11.4.3
EXISTENCE OF MINIMAL RISK ALLOCATIONS 293
11.4.4 UNIQUENESS OF OPTIMAL ALLOCATIONS 299
11.4.5 EXAMPLES OF OPTIMAL ALLOCATIONS 300
11.5 THE CAPITAL ALLOCATION PROBLEM 302
12 OPTIMAL CONTINGENT CLAIMS AND (RE)INSURANCE CONTRACTS 305
12.1 OPTIMAL CONTINGENT CLAIMS 305
12.1.1 OPTIMAL INVESTMENT PROBLEMS 306
12.1.2 MINIMAL DEMAND PROBLEM 309
12.2 OPTIMAL (RE)INSURANCE CONTRACTS 314
12.2.1 OPTIMALITY OF STOP-LOSS CONTRACTS 314
12.2.2 OPTIMAL WORST CASE (RE)INSURANCE CONTRACTS 318
IMAGE 4
XII CONTENTS
PART IV OPTIMAL PORTFOLIOS AND EXTREME
RISKS
13 OPTIMAL PORTFOLIO DIVERSIFICATION W.R.T. EXTREME RISKS 325
13.1 HEAVY-TAILED PORTFOLIOS AND MULTIVARIATE REGULAR VARIATION 325 13.2
EXTREME RISK INDEX AND PORTFOLIO DIVERSIFICATION 328
13.3 ESTIMATION OF THE EXTREME RISK INDEX AND THE OPTIMAL PORTFOLIO 333
13.4 ASYMPTOTIC NORMALITY OF 342
13.5 APPLICATION TO RISK MINIMIZATION 350
14 ORDERING OF MULTIVARIATE RISK MODELS WITH RESPECT TO EXTREME
PORTFOLIO LOSSES 353
14.1 ASYMPTOTIC PORTFOLIO LOSS ORDERING 353
14.2 CHARACTERIZATION OF ; AP| IN MULTIVARIATE REGULARLY VARYING MODELS
359
14.2.1 MULTIVARIATE REGULAR VARIATION 359
14.2.2 ORDERING OF CANONICAL SPECTRAL MEASURES 365
14.2.3 UNBALANCED TAILS 372
14.3 RELATIONS TO THE CONVEX AND SUPERMODULAR ORDER 374
14.4 EXAMPLES OF APL-ORDERING 379
REFERENCES 385
LIST OF SYMBOLS 399
INDEX 401 |
| any_adam_object | 1 |
| author | Rüschendorf, Ludger 1948- |
| author_GND | (DE-588)10867472X |
| author_facet | Rüschendorf, Ludger 1948- |
| author_role | aut |
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| author_variant | l r lr |
| building | Verbundindex |
| bvnumber | BV040710781 |
| classification_rvk | SK 980 |
| classification_tum | MAT 606f WIR 160f |
| ctrlnum | (OCoLC)844027744 (DE-599)DNB1025398823 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| indexdate | 2024-08-21T00:30:49Z |
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| isbn | 3642335896 9783642335891 |
| language | English |
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| physical | XII, 408 S. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
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| series2 | Springer series in operations research and financial engineering |
| spelling | Rüschendorf, Ludger 1948- Verfasser (DE-588)10867472X aut Mathematical risk analysis dependence, risk bounds, optimal allocations and portfolios Ludger Rüschendorf Berlin [u.a.] Springer 2013 XII, 408 S. txt rdacontent n rdamedia nc rdacarrier Springer series in operations research and financial engineering Risikotheorie (DE-588)4135592-1 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Risikotheorie (DE-588)4135592-1 s Stochastisches Modell (DE-588)4057633-4 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-33590-7 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4107640&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025691122&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rüschendorf, Ludger 1948- Mathematical risk analysis dependence, risk bounds, optimal allocations and portfolios Risikotheorie (DE-588)4135592-1 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| subject_GND | (DE-588)4135592-1 (DE-588)4057633-4 |
| title | Mathematical risk analysis dependence, risk bounds, optimal allocations and portfolios |
| title_auth | Mathematical risk analysis dependence, risk bounds, optimal allocations and portfolios |
| title_exact_search | Mathematical risk analysis dependence, risk bounds, optimal allocations and portfolios |
| title_full | Mathematical risk analysis dependence, risk bounds, optimal allocations and portfolios Ludger Rüschendorf |
| title_fullStr | Mathematical risk analysis dependence, risk bounds, optimal allocations and portfolios Ludger Rüschendorf |
| title_full_unstemmed | Mathematical risk analysis dependence, risk bounds, optimal allocations and portfolios Ludger Rüschendorf |
| title_short | Mathematical risk analysis |
| title_sort | mathematical risk analysis dependence risk bounds optimal allocations and portfolios |
| title_sub | dependence, risk bounds, optimal allocations and portfolios |
| topic | Risikotheorie (DE-588)4135592-1 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| topic_facet | Risikotheorie Stochastisches Modell |
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