Modern actuarial risk theory: using R
Gespeichert in:
| Format: | Elektronisch E-Book |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
2009
|
| Ausgabe: | 2. ed., corr. 2. print. |
| Schlagworte: | |
| Online-Zugang: | BTU01 FAN01 FHA01 FHM01 FHN01 FHR01 FKE01 FNU01 HWR01 UBG01 UBR01 UBT01 UBY01 UPA01 Volltext Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 361 - 366 |
| Beschreibung: | 1 Online-Ressource (XVIII, 381 S.) graph. Darst. |
| ISBN: | 9783540709985 9783642034077 |
| DOI: | 10.1007/978-3-540-70998-5 |
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Datensatz im Suchindex
| _version_ | 1804140749822885888 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
THERE ARE IO 11 STARS IN THE GALAXY. THAT USED TO BE A HUGE NUMBER. BUT
IT S ONLY A HUNDRED BILLION. IT S LESS THAN THE NATIONAL DEFICIT! WE
USED TO CALL THEM ASTRONOMICAL NUMBERS. NOW WE SHOULD CALL THEM
ECONOMICAL NUMBERS -
RICHARD FEYNMAN (1918-1988)
1 UTILITY THEORY AND INSURANCE 1
1 . 1 INTRODUCTION 1
1.2 THE EXPECTED UTILITY MODEL 2
1.3 CLASSES OF UTILITY FUNCTIONS 5
1.4 STOP-LOSS REINSURANCE 8
1.5 EXERCISES 14
2 THE INDIVIDUAL RISK MODEL 17
2.1 INTRODUCTION 17
2.2 MIXED DISTRIBUTIONS AND RISKS 18
2.3 CONVOLUTION 25
2.4 TRANSFORMS 28
2.5 APPROXIMATIONS 30
2.5.1 NORMAL APPROXIMATION 30
2.5.2 TRANSLATED GAMMA APPROXIMATION 32
2.5.3 NP APPROXIMATION 33
2.6 APPLICATION: OPTIMAL REINSURANCE 35
2.7 EXERCISES 36
3 COLLECTIVE RISK MODELS 41
3. 1 INTRODUCTION 41
3.2 COMPOUND DISTRIBUTIONS 42
3.2.1 CONVOLUTION FORMULA FOR A COMPOUND CDF 44
3.3 DISTRIBUTIONS FOR THE NUMBER OF CLAIMS 45
3.4 PROPERTIES OF COMPOUND POISSON DISTRIBUTIONS 47
3.5 PANJER S RECURSION 49
3.6 COMPOUND DISTRIBUTIONS AND THE FAST FOURIER TRANSFORM 54 3.7
APPROXIMATIONS FOR COMPOUND DISTRIBUTIONS 57
3.8 INDIVIDUAL AND COLLECTIVE RISK MODEL 59
3.9 LOSS DISTRIBUTIONS: PROPERTIES, ESTIMATION, SAMPLING 61 3.9.1
TECHNIQUES TO GENERATE PSEUDO-RANDOM SAMPLES 62 3.9.2 TECHNIQUES TO
COMPUTE ML-ESTIMATES 63
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/995947694
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
3.9.3 POISSON CLAIM NUMBER DISTRIBUTION 63
3.9.4 NEGATIVE BINOMIAL CLAIM NUMBER DISTRIBUTION 64
3.9.5 GAMMA CLAIM SEVERITY DISTRIBUTIONS 66
3.9.6 INVERSE GAUSSIAN CLAIM SEVERITY DISTRIBUTIONS 67
3.9.7 MIXTURES/COMBINATIONS OF EXPONENTIAL DISTRIBUTIONS 69 3.9.8
LOGNORMAL CLAIM SEVERITIES 71
3.9.9 PARETO CLAIM SEVERITIES 72
3.10 STOP-LOSS INSURANCE AND APPROXIMATIONS 73
3.10.1 COMPARING STOP-LOSS PREMIUMS IN CASE OF UNEQUAL VARIANCES 76 3.11
EXERCISES 78
RUIN THEORY 87
4.1 INTRODUCTION 87
4.2 THE CLASSICAL RUIN PROCESS 89
4.3 SOME SIMPLE RESULTS ON RUIN PROBABILITIES 91
4.4 RUIN PROBABILITY AND CAPITAL AT RUIN 95
4.5 DISCRETE TIME MODEL 98
4.6 REINSURANCE AND RUIN PROBABILITIES 99
4.7 BEEKMAN S CONVOLUTION FORMULA 101
4.8 EXPLICIT EXPRESSIONS FOR RUIN PROBABILITIES 106
4.9 APPROXIMATION OF RUIN PROBABILITIES 108
4.10 EXERCISES I LL
PREMIUM PRINCIPLES AND RISK MEASURES 115
5.1 INTRODUCTION 115
5.2 PREMIUM CALCULATION FROM TOP-DOWN 116
5.3 VARIOUS PREMIUM PRINCIPLES AND THEIR PROPERTIES 119
5.3.1 PROPERTIES OF PREMIUM PRINCIPLES 120
5.4 CHARACTERIZATIONS OF PREMIUM PRINCIPLES 122
5.5 PREMIUM REDUCTION BY COINSURANCE 125
5.6 VALUE-AT-RISK AND RELATED RISK MEASURES 126
5.7 EXERCISES 133
BONUS-MAINS SYSTEMS 135
6.1 INTRODUCTION 135
6.2 A GENERIC BONUS-MALUS SYSTEM 136
6.3 MARKOV ANALYSIS 138
6.3.1 LOIMARANTAEFFICIENCY 141
6.4 FINDING STEADY STATE PREMIUMS AND LOIMARANTA EFFICIENCY 142 6.5
EXERCISES 146
ORDERING OF RISKS 149
7.1 INTRODUCTION 149
7.2 LARGER RISKS 152
7.3 MORE DANGEROUS RISKS 154
7.3.1 THICKER-TAILED RISKS 154
7.3.2 STOP-LOSS ORDER 159
7.3.3 EXPONENTIAL ORDER 160
IMAGE 3
CONTENTS XVII
7.3.4 PROPERTIES OF STOP-LOSS ORDER 160
7.4 APPLICATIONS 164
7.4.1 INDIVIDUAL VERSUS COLLECTIVE MODEL 164
7.4.2 RUIN PROBABILITIES AND ADJUSTMENT COEFFICIENTS 164 7.4.3 ORDER IN
TWO-PARAMETER FAMILIES OF DISTRIBUTIONS 166 7.4.4 OPTIMAL REINSURANCE
168
7.4.5 PREMIUMS PRINCIPLES RESPECTING ORDER 169
7.4.6 MIXTURES OF POISSON DISTRIBUTIONS 169
7.4.7 SPREADING OF RISKS 170
7.4.8 TRANSFORMING SEVERAL IDENTICAL RISKS 170
7.5 INCOMPLETE INFORMATION 171
7.6 COMONOTONIC RANDOM VARIABLES 176
7.7 STOCHASTIC BOUNDS ON SUMS OF DEPENDENT RISKS 183
7.7.1 SHARPER UPPER AND LOWER BOUNDS DERIVED FROM A SURROGATE .. 183
7.7.2 SIMULATING STOCHASTIC BOUNDS FOR SUMS OF LOGNORMAL RISKS .. 186
7.8 MORE RELATED JOINT DISTRIBUTIONS; COPULAS 190
7.8.1 MORE RELATED DISTRIBUTIONS; ASSOCIATION MEASURES 190 7.8.2 COPULAS
194
7.9 EXERCISES 196
8 CREDIBILITY THEORY 203
8.1 INTRODUCTION 203
8.2 THE BALANCED BIIHLMANN MODEL 204
8.3 MORE GENERAL CREDIBILITY MODELS 211
8.4 THE BIIHLMANN-STRAUB MODEL 214
8.4.1 PARAMETER ESTIMATION IN THE BIIHLMANN-STRAUB MODEL 217 8.5
NEGATIVE BINOMIAL MODEL FOR THE NUMBER OF CAR INSURANCE CLAIMS . .. 222
8.6 EXERCISES 227
9 GENERALIZED LINEAR MODELS 231
9.1 INTRODUCTION 231
9.2 GENERALIZED LINEAR MODELS 234
9.3 SOME TRADITIONAL ESTIMATION PROCEDURES AND GLMS 237 9.4 DEVIANCE AND
SCALED DEVIANCE 245
9.5 CASE STUDY I: ANALYZING A SIMPLE AUTOMOBILE PORTFOLIO 248 9.6 CASE
STUDY II: ANALYZING A BONUS-MALUS SYSTEM USING GLM 252 9.6.1 GLM
ANALYSIS FOR THE TOTAL CLAIMS PER POLICY 257
9.7 EXERCISES 262
10 IBNR TECHNIQUES 265
10.1 INTRODUCTION 265
10.2 TWO TIME-HONORED IBNR METHODS 268
10.2.1 CHAIN LADDER 268
10.2.2 BORNHUETTER-FERGUSON 270
10.3 A GLM THAT ENCOMPASSES VARIOUS IBNR METHODS 271 10.3.1 CHAIN LADDER
METHOD AS A GLM 272
IMAGE 4
XVIII CONTENTS
10.3.2 ARITHMETIC AND GEOMETRIC SEPARATION METHODS 273 10.3.3 DE
VIJLDER S LEAST SQUARES METHOD 274
10.4 ILLUSTRATION OF SOME IBNR METHODS 276
10.4.1 MODELING THE CLAIM NUMBERS IN TABLE 10.1 277
10.4.2 MODELING CLAIM SIZES 279
10.5 SOLVING IBNR PROBLEMS BY R 282
10.6 VARIABILITY OF THE IBNR ESTIMATE 284
10.6.1 BOOTSTRAPPING 285
10.6.2 ANALYTICAL ESTIMATE OF THE PREDICTION ERROR 288
10.7 AN IBNR-PROBLEM WITH KNOWN EXPOSURES 290
10.8 EXERCISES 292
11 MORE ON GLMS 297
11.1 INTRODUCTION 297
11.2 LINEAR MODELS AND GENERALIZED LINEAR MODELS 297
11.3 THE EXPONENTIAL DISPERSION FAMILY 300
11.4 FITTING CRITERIA 305
11.4.1 RESIDUALS 305
11.4.2 QUASI-LIKELIHOOD AND QUASI-DEVIANCE 306
11.4.3 EXTENDED QUASI-LIKELIHOOD 308
11.5 THE CANONICAL LINK 310
11.6 THE IRLS ALGORITHM OF NEIDER AND WEDDERBURN 312
11.6.1 THEORETICAL DESCRIPTION 313
11.6.2 STEP-BY-STEP IMPLEMENTATION 315
11.7 TWEEDIE S COMPOUND POISSON-GAMMA DISTRIBUTIONS 317 11.7.1
APPLICATION TO AN IBNR PROBLEM 318
11.8 EXERCISES 320
THE R IN MODERN ART 325
A. 1 A SHORT INTRODUCTION TO R 325
A.2 ANALYZING A STOCK PORTFOLIO USING R 332
A.3 GENERATING A PSEUDO-RANDOM INSURANCE PORTFOLIO 338
HINTS FOR THE EXERCISES 341
NOTES AND REFERENCES 357
TABLES 367
INDEX 371
|
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| discipline | Soziologie Mathematik Wirtschaftswissenschaften |
| doi_str_mv | 10.1007/978-3-540-70998-5 |
| edition | 2. ed., corr. 2. print. |
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| id | DE-604.BV035803029 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:04:56Z |
| institution | BVB |
| isbn | 9783540709985 9783642034077 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018662121 |
| oclc_num | 638514878 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG DE-739 DE-1102 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-M347 DE-703 DE-1049 DE-634 DE-Aug4 DE-2070s DE-859 DE-706 DE-92 |
| owner_facet | DE-473 DE-BY-UBG DE-739 DE-1102 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-M347 DE-703 DE-1049 DE-634 DE-Aug4 DE-2070s DE-859 DE-706 DE-92 |
| physical | 1 Online-Ressource (XVIII, 381 S.) graph. Darst. |
| psigel | ZDB-2-SBE |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| spelling | Modern actuarial risk theory using R Rob Kaas ... 2. ed., corr. 2. print. Berlin ; Heidelberg Springer 2009 1 Online-Ressource (XVIII, 381 S.) graph. Darst. txt rdacontent c rdamedia cr rdacarrier Literaturverz. S. 361 - 366 Versicherungsmathematik (DE-588)4063194-1 gnd rswk-swf Risikotheorie (DE-588)4135592-1 gnd rswk-swf Risikotheorie (DE-588)4135592-1 s Versicherungsmathematik (DE-588)4063194-1 s DE-604 Kaas, R. Sonstige (DE-588)171299949 oth https://doi.org/10.1007/978-3-540-70998-5 Verlag Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018662121&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Modern actuarial risk theory using R Versicherungsmathematik (DE-588)4063194-1 gnd Risikotheorie (DE-588)4135592-1 gnd |
| subject_GND | (DE-588)4063194-1 (DE-588)4135592-1 |
| title | Modern actuarial risk theory using R |
| title_auth | Modern actuarial risk theory using R |
| title_exact_search | Modern actuarial risk theory using R |
| title_full | Modern actuarial risk theory using R Rob Kaas ... |
| title_fullStr | Modern actuarial risk theory using R Rob Kaas ... |
| title_full_unstemmed | Modern actuarial risk theory using R Rob Kaas ... |
| title_short | Modern actuarial risk theory |
| title_sort | modern actuarial risk theory using r |
| title_sub | using R |
| topic | Versicherungsmathematik (DE-588)4063194-1 gnd Risikotheorie (DE-588)4135592-1 gnd |
| topic_facet | Versicherungsmathematik Risikotheorie |
| url | https://doi.org/10.1007/978-3-540-70998-5 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018662121&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kaasr modernactuarialrisktheoryusingr |