Holdings: Modern actuarial risk theory

Modern actuarial risk theory: using R

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Bibliographic Details
Format:	Electronic eBook
Language:	English
Published:	Berlin [u.a.] Springer 2008
Edition:	2. ed., corr. 2. print.
Subjects:	Versicherungsmathematik Risikotheorie
Online Access:	BTU01 FAN01 FHI01 FHM01 FHR01 FKE01 FNU01 HWR01 UBG01 UBR01 UBT01 UBY01 UPA01 Volltext Inhaltsverzeichnis
Physical Description:	1 Online-Ressource (XVIII, 381 S.) graph. Darst.
ISBN:	9783540709985
DOI:	10.1007/978-3-540-70998-5

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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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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
work_keys_str_mv	AT kaasr modernactuarialrisktheoryusingr

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