Non-life insurance pricing with generalized linear models:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2010
|
| Schriftenreihe: | EAA series/EAA Lecture Notes
EAA series - textbook |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XIII, 174 S. graph. Darst. |
| ISBN: | 9783642107900 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text |
IX CONTENTS 1 NON-LIFE INSURANCE PRICING 1 1.1 RATING FACTORS AND KEY
RATIOS 2 1.2 BASIC MODEL ASSUMPTIONS 6 1.2.1 MEANS AND VARIANCES 8 1.3
MULTIPLICATIVE MODELS 9 1.3.1 THE METHOD OF MARGINAL TOTALS 11 1.3.2 ONE
FACTOR AT A TIME? 12 EXERCISES 13 2 THE BASICS OF PRICING WITH GLMS 15
2.1 EXPONENTIAL DISPERSION MODELS 16 2.1.1 PROBABILITY DISTRIBUTION OF
THE CLAIM FREQUENCY 18 2.1.2 A MODEL FOR CLAIM SEVERITY 20 2.1.3
CUMULANT-GENERATING FUNCTION, EXPECTATION AND VARIANCE . 21 2.1.4
TWEEDIE MODELS 24 2.2 THE LINK FUNCTION 26 2.2.1 CANONICAL LINK* 29 2.3
PARAMETER ESTIMATION 30 2.3.1 THE MULTIPLICATIVE POISSON MODEL 30 2.3.2
GENERAL RESULT 31 2.3.3 MULTIPLICATIVE GAMMA MODEL FOR CLAIM SEVERITY 33
2.3.4 MODELING THE PURE PREMIUM 34 2.4 CASE STUDY: MOTORCYCLE INSURANCE
35 EXERCISES 37 3 GLM MODEL BUILDING 39 3.1 HYPOTHESIS TESTING AND
ESTIMATION OF 39 3.1.1 PEARSON'S CHI-SQUARE AND THE ESTIMATION OF 42
3.1.2 TESTING HIERARCHICAL MODELS 43 3.2 CONFIDENCE INTERVALS BASED ON
FISHER INFORMATION 44 3.2.1 FISHER INFORMATION 44 3.2.2 CONFIDENCE
INTERVALS 45 BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1000034526
DIGITALISIERT DURCH CONTENTS 3.2.3 NUMERICAL EQUATION SOLVING* 49 3.2.4
DO THE ML EQUATIONS REALLY GIVE A MAXIMUM?* 50 3.2.5 ASYMPTOTIC
NORMALITY OF THE ML ESTIMATORS* 51 3.3 RESIDUALS 53 3.4 OVERDISPERSION .
54 3.5 ESTIMATION WITHOUT DISTRIBUTIONAL ASSUMPTIONS 58 3.5.1 ESTIMATING
EQUATIONS 58 3.5.2 THE OVERDISPERSED POISSON MODEL 60 3.5.3 DEFINING
DEVIANCES FROM VARIANCE FUNCTIONS* 60 3.6 MISCELLANEA 61 3.6.1 MODEL
SELECTION 61 3.6.2 INTERACTION 62 3.6.3 OFFSETS 63 3.6.4 POLYNOMIAL
REGRESSION 63 3.6.5 LARGE CLAIMS 63 3.6.6 DEDUCTIBLES* 64 3.6.7
DETERMINING THE PREMIUM LEVEL 65 3.7 CASE STUDY: MODEL SELECTION IN MC
INSURANCE 66 EXERCISES 66 MULTI-LEVEL FACTORS AND CREDIBILITY THEORY 71
4.1 THE BIIHLMANN-STRAUB MODEL 74 4.1.1 ESTIMATION OF VARIANCE
PARAMETERS 78 4.1.2 COMPARISON WITH OTHER NOTATION* 81 4.2 CREDIBILITY
ESTIMATORS IN MULTIPLICATIVE MODELS 81 4.2.1 ESTIMATION OF VARIANCE
PARAMETERS 84 4.2.2 THE BACKFILLING ALGORITHM 84 4.2.3 APPLICATION TO
CAR MODEL CLASSIFICATION 86 4.2.4 MORE THAN ONE MLF 87 4.3 EXACT
CREDIBILITY* 89 4.4 HIERARCHICAL CREDIBILITY MODELS 90 4.4.1 ESTIMATION
OF VARIANCE PARAMETERS 94 4.4.2 CAR MODEL CLASSIFICATION, THE
HIERARCHICAL CASE 95 4.5 CASE STUDY: BUS INSURANCE 96 EXERCISES 97
GENERALIZED ADDITIVE MODELS 101 5. CONTENTS XI 5.4.3 GAMMA CASE 120 5.5
CHOOSING THE SMOOTHING PARAMETER 121 5.6 INTERACTION BETWEEN A
CONTINUOUS AND A CATEGORICAL VARIABLE . 124 5.7 BIVARIATE SPLINES 125
5.7.1 THIN PLATE SPLINES 126 5.7.2 ESTIMATION WITH THIN PLATE SPLINES
127 5.8 CASE STUDY: TRYING GAMS IN MOTOR INSURANCE 132 EXERCISES 133 A
SOME RESULTS FROM PROBABILITY AND STATISTICS 135 A.I THE GAMMA FUNCTION
135 A.2 CONDITIONAL EXPECTATION 135 A.3 THE LAW OF TOTAL PROBABILITY 136
A.4 BAYES' THEOREM 137 A.5 UNBIASED ESTIMATION OF WEIGHTED VARIANCES 138
B SOME RESULTS ON SPLINES 139 B.I CUBIC SPLINES 139 B.2 B-SPLINES 145
B.3 THIN PLATE SPLINES 152 C SOME SAS SYNTAX 165 C.I PARAMETER
ESTIMATION WITH PROC GENMOD 165 C.2 ESTIMATION OF AND TESTING 166 C.3
SAS SYNTAX FOR ARBITRARY DEVIANCE* 167 C.4 BACKFITTING OF MLFS 168 C.5
FITTING GAMS 168 C.6 MISCELLANEA 168 REFERENCES 171 INDEX 173 |
| any_adam_object | 1 |
| author | Ohlsson, Esbjörn Johansson, Björn |
| author_facet | Ohlsson, Esbjörn Johansson, Björn |
| author_role | aut aut |
| author_sort | Ohlsson, Esbjörn |
| author_variant | e o eo b j bj |
| building | Verbundindex |
| bvnumber | BV025599733 |
| classification_rvk | QQ 630 SK 980 |
| ctrlnum | (OCoLC)845690776 (DE-599)BVBBV025599733 |
| dewey-full | 368.011 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 368 - Insurance |
| dewey-raw | 368.011 |
| dewey-search | 368.011 |
| dewey-sort | 3368.011 |
| dewey-tens | 360 - Social problems and services; associations |
| discipline | Soziologie Mathematik Wirtschaftswissenschaften |
| format | Book |
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| indexdate | 2024-07-20T10:34:48Z |
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| isbn | 9783642107900 |
| language | English |
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| spelling | Ohlsson, Esbjörn Verfasser aut Non-life insurance pricing with generalized linear models Esbjörn Ohlsson ; Björn Johansson Berlin [u.a.] Springer 2010 XIII, 174 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier EAA series/EAA Lecture Notes EAA series - textbook Versicherungsprämie (DE-588)4063198-9 gnd rswk-swf Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd rswk-swf Versicherungsmathematik (DE-588)4063194-1 gnd rswk-swf Versicherungsprämie (DE-588)4063198-9 s Versicherungsmathematik (DE-588)4063194-1 s Verallgemeinertes lineares Modell (DE-588)4124382-1 s DE-604 Johansson, Björn Verfasser aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3423856&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=020195297&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ohlsson, Esbjörn Johansson, Björn Non-life insurance pricing with generalized linear models Versicherungsprämie (DE-588)4063198-9 gnd Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd Versicherungsmathematik (DE-588)4063194-1 gnd |
| subject_GND | (DE-588)4063198-9 (DE-588)4124382-1 (DE-588)4063194-1 |
| title | Non-life insurance pricing with generalized linear models |
| title_auth | Non-life insurance pricing with generalized linear models |
| title_exact_search | Non-life insurance pricing with generalized linear models |
| title_full | Non-life insurance pricing with generalized linear models Esbjörn Ohlsson ; Björn Johansson |
| title_fullStr | Non-life insurance pricing with generalized linear models Esbjörn Ohlsson ; Björn Johansson |
| title_full_unstemmed | Non-life insurance pricing with generalized linear models Esbjörn Ohlsson ; Björn Johansson |
| title_short | Non-life insurance pricing with generalized linear models |
| title_sort | non life insurance pricing with generalized linear models |
| topic | Versicherungsprämie (DE-588)4063198-9 gnd Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd Versicherungsmathematik (DE-588)4063194-1 gnd |
| topic_facet | Versicherungsprämie Verallgemeinertes lineares Modell Versicherungsmathematik |
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