On infinitely divisible random fields with an application in insurance:
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| Main Author: | |
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| Format: | Thesis Book |
| Language: | English |
| Published: |
2012
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zsfassung in dt. Sprache |
| Physical Description: | IX, 262 S. Ill., graph. Darst. |
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| 245 | 1 | 0 | |a On infinitely divisible random fields with an application in insurance |c vorgelegt von Wolfgang Karcher |
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Record in the Search Index
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| adam_text | IMAGE 1
CONTENTS
NOMENCLATURE VII
1. INTRODUCTION 1
1.1. MOTIVATION 1
1.2. OUTLINE 5
2. PRELIMINARIES 9
2.1. INFINITELY DIVISIBLE DISTRIBUTIONS 9
2.1.1. DEFINITION AND BASIC PROPERTIES 9
2.1.2. STABLE DISTRIBUTIONS 17
2.2. MAX-INFINITELY DIVISIBLE DISTRIBUTIONS 25
2.2.1. DEFINITION AND BASIC PROPERTIES 25
2.2.2. MAX-STABLE DISTRIBUTIONS 28
2.3. INFINITELY DIVISIBLE RANDOM MEASURES AND STOCHASTIC INTEGRALS 31
2.3.1. GENERAL INFINITELY DIVISIBLE RANDOM MEASURES AND STOCHASTIC
INTEGRALS 31
2.3.2. STABLE STOCHASTIC INTEGRALS 39
2.4. RANDOM FIELDS 43
2.5. INFINITELY DIVISIBLE RANDOM FIELDS 47
2.5.1. INFINITELY DIVISIBLE RANDOM FIELDS WITH SPECTRAL REPRESENTATION .
. . . 47
2.5.2. STABLE RANDOM FIELDS WITH SPECTRAL REPRESENTATION 55
2.6. MAX-INFINITELY DIVISIBLE RANDOM FIELDS 57
2.6.1. MAX-INFINITELY DIVISIBLE RANDOM FIELDS WITH SPECTRAL
REPRESENTATION . 57 2.6.2. MAX-STABLE RANDOM FIELDS WITH SPECTRAL
REPRESENTATION 58
3. TOOLS FOR INFINITELY DIVISIBLE RANDOM FIELDS WITH SPECTRAL
REPRESENTATION 6 1
3.1. SIMULATION OF INFINITELY DIVISIBLE RANDOM FIELDS 61
3.1.1. APPROXIMATION OF INFINITELY DIVISIBLE RANDOM FIELDS WITH SPECTRAL
REP RESENTATION 62
3.1.2. MEASURING THE APPROXIMATION ERROR 64
III
HTTP://D-NB.INFO/103023969X
IMAGE 2
CONTENTS
3.1.3. STEP FUNCTION APPROXIMATION 69
3.1.4. APPROXIMATION BY HAAR WAVELET SERIES 73
3.1.5. SIMULATION STUDY 87
3.1.6. DISCUSSION 92
3.2. EXTRAPOLATION OF STABLE RANDOM FIELDS 93
3.2.1. LEAST SCALE LINEAR (LSL) PREDICTOR 95
3.2.2. COVARIATION ORTHOGONAL LINEAR (COL) PREDICTOR 98
3.2.3. MAXIMIZATION OF COVARIATION LINEAR (MCL) PREDICTOR 104
3.2.4. NUMERICAL RESULTS I L L
3.2.5. DISCUSSION 113
3.3. NON-PARAMETRIC ESTIMATION OF THE KERNEL FUNCTION FOR INFINITELY
DIVISIBLE RAN DOM FIELDS 115
3.3.1. INFINITELY DIVISIBLE RANDOM FIELDS WITH SECOND MOMENT 115
3.3.2. STABLE RANDOM FIELDS 124
3.3.3. DISCUSSION 135
3.4. ESTIMATION OF THE CHARACTERISTIC TRIPLET OF THE INFINITELY
DIVISIBLE RANDOM MEASURE 136
3.4.1. METHOD OF MOMENTS 136
3.4.2. NON-PARAMETRIC ESTIMATION 138
3.4.3. SOME NUMERICAL RESULTS 149
3.4.4. DISCUSSION 155
3.5. CENTRAL LIMIT THEOREMS FOR THE EXCURSION SETS VOLUME OF RANDOM
FIELDS . . . . 160
3.5.1. CENTRAL LIMIT THEOREM 162
3.5.2. STATISTICAL TEST 172
3.5.3. COVARIANCE ESTIMATES FOR THE CLT 175
3.5.4. FUNCTIONAL CENTRAL LIMIT THEOREM 188
3.5.5. COVARIANCE ESTIMATES FOR THE FUNCTIONAL CLT 190
3.5.6. DISCUSSION 202
4. APPLICATION IN INSURANCE 2 0 3
4.1. DATA DESCRIPTION AND ANALYSIS 204
4.2. SPATIAL MODELING 207
4.2.1. A MODEL FOR THE CLAIM SIZES 208
4.2.2. MODEL FITTING 209
4.3. SPATIAL PREMIUM RATING 212
4.4. RISK MAPPING 213
IV
IMAGE 3
CONTENTS
4.5. DISCUSSION 214
A. TECHNICAL DETAILS 2 1 7
A.L. PROOF OF REMARK 3.10 217
A.2. PROOF OF REMARK 3.21 221
A.2.1. ONE-DIMENSIONAL CASE 221
A.2.2. MULTIDIMENSIONAL CASE 229
A.3. PROOF OF REMARK 3.43 239
BIBLIOGRAPHY 2 4 1
LIST O F FIGURES 2 5 3
LIST O F TABLES 2 5 5
INDEX 2 5 7
ZUSAMMENFASSUNG 2 5 9
ACKNOWLEDGEMENTS 2 6 1
V
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| any_adam_object | 1 |
| author | Karcher, Wolfgang |
| author_GND | (DE-588)1030239533 |
| author_facet | Karcher, Wolfgang |
| author_role | aut |
| author_sort | Karcher, Wolfgang |
| author_variant | w k wk |
| building | Verbundindex |
| bvnumber | BV040746787 |
| ctrlnum | (OCoLC)828801868 (DE-599)BSZ377217638 |
| dewey-full | 519.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.23 |
| dewey-search | 519.23 |
| dewey-sort | 3519.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| indexdate | 2024-07-10T00:33:04Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025726591 |
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| physical | IX, 262 S. Ill., graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
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| spelling | Karcher, Wolfgang Verfasser (DE-588)1030239533 aut On infinitely divisible random fields with an application in insurance vorgelegt von Wolfgang Karcher 2012 IX, 262 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Zsfassung in dt. Sprache Ulm, Univ., Diss., 2012 Random fields Zufälliges Feld (DE-588)4191094-1 gnd rswk-swf Teilbarkeit (DE-588)4203392-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Zufälliges Feld (DE-588)4191094-1 s Teilbarkeit (DE-588)4203392-5 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025726591&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Karcher, Wolfgang On infinitely divisible random fields with an application in insurance Random fields Zufälliges Feld (DE-588)4191094-1 gnd Teilbarkeit (DE-588)4203392-5 gnd |
| subject_GND | (DE-588)4191094-1 (DE-588)4203392-5 (DE-588)4113937-9 |
| title | On infinitely divisible random fields with an application in insurance |
| title_auth | On infinitely divisible random fields with an application in insurance |
| title_exact_search | On infinitely divisible random fields with an application in insurance |
| title_full | On infinitely divisible random fields with an application in insurance vorgelegt von Wolfgang Karcher |
| title_fullStr | On infinitely divisible random fields with an application in insurance vorgelegt von Wolfgang Karcher |
| title_full_unstemmed | On infinitely divisible random fields with an application in insurance vorgelegt von Wolfgang Karcher |
| title_short | On infinitely divisible random fields with an application in insurance |
| title_sort | on infinitely divisible random fields with an application in insurance |
| topic | Random fields Zufälliges Feld (DE-588)4191094-1 gnd Teilbarkeit (DE-588)4203392-5 gnd |
| topic_facet | Random fields Zufälliges Feld Teilbarkeit Hochschulschrift |
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