Applying robust scale M-estimators to compute credibility premiums in the large claim case:
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| Main Author: | |
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| Format: | Thesis Book |
| Language: | English |
| Published: |
Berlin
Logos-Verl.
2008
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| Subjects: | |
| Online Access: | Beschreibung für Leser Inhaltsverzeichnis |
| Physical Description: | IX, 121 S. graph. Darst. 21 cm |
| ISBN: | 9783832520373 |
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Record in the Search Index
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| adam_text |
APPLYING ROBUST SCALE M-ESTIMATORS TO COMPUTE CREDIBILITY PREMIUMS IN
THE LARGE CLAIM CASE VOM FACHBEREICH MATHEMATIK DER TECHNISCHEN
UNIVERSITAT DARMSTADT ZUR ERLANGUNG DES GRADES EINES DOKTORS DER
NATURWISSENSCHAFTEN (DR.RER. NAT.) GENEHMIGTE DISSERTATION VON
DIPL.-MATH. ANNETT KELLER AUS DRESDEN REFERENT: PROF. DR. J. LEHN
KORREFERENTEN PROF. DR. A. MAY PROF. DR. M. KOHLER TAG DER EINREICHUNG:
27. FEBRUAR 2008 TAG DER MIINDLICHEN PRIIFUNG: 27. MAI 2008 DARMSTADT
2008 D 17 CONTENTS INTRODUCTION 1 1 PRELIMINARIES 5 1.1 THE TERM
INSURANCE PREMIUM 5 1.2 CREDIBILITY PREMIUM 6 1.2.1 A SHORT SURVEY OF
CREDIBILITY 6 1.2.2 CREDIBILITY IN THE SENSE OF BIIHLMANN 7 1.3 A SHORT
SURVEY OF ROBUST STATISTICS 10 1.3.1 QUALITATIVE ROBUSTNESS 11 1.3.2
QUANTITATIVE ROBUSTNESS 12 1.4 THE MODEL SETTING 13 2 ROBUST ESTIMATION
17 2.1 ESTIMATORS AS FUNCTIONALS 17 2.2 M-ESTIMATORS 18 2.2.1 DEFINITION
OF A LOCATION M-ESTIMATOR 20 2.2.2 DEFINITION OF A SCALE M-ESTIMATOR 22
2.2.3 FISHER-CONSISTENT M-ESTIMATORS 24 2.3 MAIN CONCEPTS IN
QUANTITATIVE ROBUSTNESS 25 2.3.1 INFLUENCE FUNCTIONS OF M-ESTIMATORS 28
2.3.2 SOME PROPERTIES OF INFLUENCE FUNCTIONS 31 2.3.3 THE ASYMPTOTIC
VARIANCE OF T N 32 2.4 DEFINING ROBUST M-ESTIMATORS USING THE INFLUENCE
FUNCTION 34 3 ROBUST ESTIMATORS IN THE F-MODEL 43 3.1 THE M-ESTIMATOR IN
THE T-MODEL 43 3.2 THE ESTIMATOR T N I 45 3.2.1 CONSISTENCY OF THE
ESTIMATOR T N ,J 46 3.2.2 THE INFLUENCE FUNCTIONS OF T AND F 52 3.3 THE
OPTIMAL CHOICE FOR A 54 3.3.1 DERIVING A ACCORDING TO LEMMA 2.10 54
3.3.2 THE MINIMUM VARIANCE APPROACH 57 4 QUANTITATIVE CHARACTERISTICS OF
T N AND T N 67 4.1 ASYMPTOTIC NORMALITY OF T N _J AND X NJ J 67 4.2
GROSS ERROR 70 4.3 FINITE SAMPLE BREAKDOWN POINTS AND AN OPTIMAL CHOICE
FOR 6 73 5 ESTIMATION AND SIMULATION 77 5.1 ESTIMATING T N ,; AND T N ,
77 5.2 SIMULATION STUDY 91 5.3 CREDIBILITY PREMIUM 96 CONCLUSION AND
OUTLOOK 103 APPENDIX 107 |
| any_adam_object | 1 |
| author | Keller, Annett 1978- |
| author_GND | (DE-588)136581617 |
| author_facet | Keller, Annett 1978- |
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| dewey-full | 368.5 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 368 - Insurance |
| dewey-raw | 368.5 |
| dewey-search | 368.5 |
| dewey-sort | 3368.5 |
| dewey-tens | 360 - Social problems and services; associations |
| discipline | Wirtschaftswissenschaften |
| format | Thesis Book |
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| indexdate | 2024-07-20T10:10:04Z |
| institution | BVB |
| isbn | 9783832520373 |
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| spelling | Keller, Annett 1978- Verfasser (DE-588)136581617 aut Applying robust scale M-estimators to compute credibility premiums in the large claim case von Annett Keller Berlin Logos-Verl. 2008 IX, 121 S. graph. Darst. 21 cm txt rdacontent n rdamedia nc rdacarrier Zugl.: Darmstadt, Techn. Univ., Diss., 2008 Schadenversicherung (DE-588)4179306-7 gnd rswk-swf Versicherungsprämie (DE-588)4063198-9 gnd rswk-swf Versicherungsmathematik (DE-588)4063194-1 gnd rswk-swf Robuste Schätzung (DE-588)4178265-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Versicherungsprämie (DE-588)4063198-9 s Robuste Schätzung (DE-588)4178265-3 s DE-604 Schadenversicherung (DE-588)4179306-7 s Versicherungsmathematik (DE-588)4063194-1 s http://deposit.dnb.de/cgi-bin/dokserv?id=3160115&prov=M&dok_var=1&dok_ext=htm Beschreibung für Leser HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017446930&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Keller, Annett 1978- Applying robust scale M-estimators to compute credibility premiums in the large claim case Schadenversicherung (DE-588)4179306-7 gnd Versicherungsprämie (DE-588)4063198-9 gnd Versicherungsmathematik (DE-588)4063194-1 gnd Robuste Schätzung (DE-588)4178265-3 gnd |
| subject_GND | (DE-588)4179306-7 (DE-588)4063198-9 (DE-588)4063194-1 (DE-588)4178265-3 (DE-588)4113937-9 |
| title | Applying robust scale M-estimators to compute credibility premiums in the large claim case |
| title_auth | Applying robust scale M-estimators to compute credibility premiums in the large claim case |
| title_exact_search | Applying robust scale M-estimators to compute credibility premiums in the large claim case |
| title_full | Applying robust scale M-estimators to compute credibility premiums in the large claim case von Annett Keller |
| title_fullStr | Applying robust scale M-estimators to compute credibility premiums in the large claim case von Annett Keller |
| title_full_unstemmed | Applying robust scale M-estimators to compute credibility premiums in the large claim case von Annett Keller |
| title_short | Applying robust scale M-estimators to compute credibility premiums in the large claim case |
| title_sort | applying robust scale m estimators to compute credibility premiums in the large claim case |
| topic | Schadenversicherung (DE-588)4179306-7 gnd Versicherungsprämie (DE-588)4063198-9 gnd Versicherungsmathematik (DE-588)4063194-1 gnd Robuste Schätzung (DE-588)4178265-3 gnd |
| topic_facet | Schadenversicherung Versicherungsprämie Versicherungsmathematik Robuste Schätzung Hochschulschrift |
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