Modern actuarial risk theory: using R
Gespeichert in:
| Format: | Elektronisch E-Book |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2008
|
| Ausgabe: | 2. ed., corr. 2. print. |
| Schlagworte: | |
| Online-Zugang: | BTU01 FAN01 FHI01 FHM01 FHR01 FKE01 FNU01 HWR01 UBG01 UBR01 UBT01 UBY01 UPA01 URL des Erstveröffentlichers Inhaltsverzeichnis |
| Beschreibung: | 1 Online-Ressource (XVIII, 381 S.) graph. Darst. |
| ISBN: | 9783540709985 |
| DOI: | 10.1007/978-3-540-70998-5 |
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Datensatz im Suchindex
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| adam_text | CONTENTS THERE ARE 10 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) 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
13 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 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. BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/989384071 DIGITALISIERT DURCH XVI 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 4 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 111 5 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 6
BONUS-MALUS SYSTEMS 135 6.1 INTRODUCTION 135 6. CONTENTS XVII 7.3.2
STOP-LOSS ORDER 159 7.3.3 EXPONENTIAL ORDER 160 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
GENERAI CREDIBILITY MODELS 211 8.4 THE BUHLMANN-STRAUB MODEL 214 8.4.1
PARAMETER ESTIMATION IN THE BUHLMANN-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. XVIII CONTENTS 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 10.3.2 ARITHMETIC
AND GEOMETRIE 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 281 10.6 VARIABILITY OF THE IBNR ESTIMATE 283
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 THEIRLSALGORITHMOFNELDERANDWEDDERBURN 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 MODEM ART 325 A.L A
SHORT INTRODUCTION TO R 325 A.2 ANALYZING A STOCK PORTFOLIO USING R 332
A.3 GENERATING A PSEUDO-RANDOM INSURANCE PORTFOLIO 338 HINT
|
| adam_txt |
CONTENTS THERE ARE 10" 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) 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
13 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 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. BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/989384071 DIGITALISIERT DURCH XVI 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 4 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 111 5 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 6
BONUS-MALUS SYSTEMS 135 6.1 INTRODUCTION 135 6. CONTENTS XVII 7.3.2
STOP-LOSS ORDER 159 7.3.3 EXPONENTIAL ORDER 160 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
GENERAI CREDIBILITY MODELS 211 8.4 THE BUHLMANN-STRAUB MODEL 214 8.4.1
PARAMETER ESTIMATION IN THE BUHLMANN-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. XVIII CONTENTS 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 10.3.2 ARITHMETIC
AND GEOMETRIE 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 281 10.6 VARIABILITY OF THE IBNR ESTIMATE 283
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 THEIRLSALGORITHMOFNELDERANDWEDDERBURN 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 MODEM ART 325 A.L A
SHORT INTRODUCTION TO R 325 A.2 ANALYZING A STOCK PORTFOLIO USING R 332
A.3 GENERATING A PSEUDO-RANDOM INSURANCE PORTFOLIO 338 HINT |
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| discipline | Informatik Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Informatik Mathematik Wirtschaftswissenschaften |
| doi_str_mv | 10.1007/978-3-540-70998-5 |
| edition | 2. ed., corr. 2. print. |
| format | Electronic eBook |
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| id | DE-604.BV035133990 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T22:25:23Z |
| indexdate | 2024-07-09T21:23:05Z |
| institution | BVB |
| isbn | 9783540709985 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016801459 |
| oclc_num | 638514878 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG DE-739 DE-706 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-M347 DE-703 DE-1102 DE-1049 DE-634 DE-2070s DE-859 DE-573 DE-188 |
| owner_facet | DE-473 DE-BY-UBG DE-739 DE-706 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-M347 DE-703 DE-1102 DE-1049 DE-634 DE-2070s DE-859 DE-573 DE-188 |
| physical | 1 Online-Ressource (XVIII, 381 S.) graph. Darst. |
| psigel | ZDB-2-SBE |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| spelling | Modern actuarial risk theory using R Rob Kaas ... 2. ed., corr. 2. print. Berlin [u.a.] Springer 2008 1 Online-Ressource (XVIII, 381 S.) graph. Darst. txt rdacontent c rdamedia cr rdacarrier 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 Erscheint auch als Druck-Ausgabe, Hardcover 978-3-540-70992-3 Erscheint auch als Druck-Ausgabe, Paperback 978-3-642-03407-7 https://doi.org/10.1007/978-3-540-70998-5 Verlag URL des Erstveröffentlichers Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016801459&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_exact_search_txtP | 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=016801459&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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