Loss models: from data to decisions
Gespeichert in:
| Hauptverfasser: | , , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ
Wiley
2008
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Wiley series in probability and statistics
|
| Schlagworte: | |
| Online-Zugang: | Cover Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references |
| Beschreibung: | XIX, 726 S. graph. Darst. |
| ISBN: | 9780470187814 |
Internformat
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Datensatz im Suchindex
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| adam_text | LOSS MODELS FROM DATA TO DECISIONS THIRD EDITION STUART A. KLUGMAN DRAKE
UNIVERSITY HARRY H. PANJER UNIVERSITY OF WATERLOO GORDON E.WILLMOT
UNIVERSITY OF WATERLOO WILEY A JOHN WILEY & SONS, INC., PUBLICATION
CONTENTS PREFACE XVII PART I INTRODUCTION 1 MODELING 3 1.1 1.2 THE
MODEL-BASED APPROACH 1.1.1 THE MODELING PROCESS 1.1.2 THE MODELING
ADVANTAGE ORGANIZATION OF THIS BOOK RANDOM VARIABLES 2.1 2.2 BASIC 3.1
3.2 3.3 INTRODUCTION KEY FUNCTIONS AND FOUR MODELS 2.2.1 EXERCISES
DISTRIBUTIONAL QUANTITIES MOMENTS 3.1.1 EXERCISES QUANTILES 3.2.1
EXERCISES GENERATING FUNCTIONS AND SUMS OF RANDOM VARIABLES 3 4 5 5 9 9
11 19 21 21 28 29 29 30 VI CONTENTS 3.4 3.5 4.1 4.2 3.3.1 EXERCISES
TAILS OF DISTRIBUTIONS 3.4.1 3.4.2 3.4.3 3.4.4 3.4.5 3.4.6
CLASSIFICATION BASED ON MOMENTS COMPARISON BASED ON LIMITING TAIL
BEHAVIOR CLASSIFICATION BASED ON THE HAZARD RATE FUNCTION CLASSIFICATION
BASED ON THE MEAN EXCESS LOSS FUNCTION EQUILIBRIUM DISTRIBUTIONS AND
TAIL BEHAVIOR EXERCISES MEASURES OF RISK 3.5.1 3.5.2 3.5.3 3.5.4 3.5.5
ITERISTI INTRODUCTION RISK MEASURES AND COHERENCE VALUE-AT-RISK
TAIL-VALUE-AT-RISK EXERCISES PART II ACTUARIAL MODELS CS OF ACTUARIAL
MODELS INTRODUCTION THE ROLE OF PARAMETERS 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5
PARAMETRIC AND SCALE DISTRIBUTIONS PARAMETRIC DISTRIBUTION FAMILIES
FINITE MIXTURE DISTRIBUTIONS DATA-DEPENDENT DISTRIBUTIONS EXERCISES 34
34 34 35 36 37 39 40 42 42 42 44 45 49 53 53 53 54 56 56 58 59
CONTINUOUS MODELS 61 61 61 62 62 64 64 68 69 70 74 74 74 74 76 77 5, .1
5.2 5. 5. .3 .4 INTRODUCTION CREATING 5.2.1 5.2.2 5.2.3 5.2.4 5.2.5
5.2.6 5.2.7 SELECTED 5.3.1 5.3.2 5.3.3 5.3.4 NEW DISTRIBUTIONS
MULTIPLICATION BY A CONSTANT RAISING TO A POWER EXPONENTIATION MIXING
FRAILTY MODELS SPLICING EXERCISES DISTRIBUTIONS AND THEIR RELATIONSHIPS
INTRODUCTION TWO PARAMETRIC FAMILIES LIMITING DISTRIBUTIONS EXERCISES
THE LINEAR EXPONENTIAL FAMILY CONTENTS VII 5.4.1 EXERCISES 79 5.5 TVAR
FOR CONTINUOUS DISTRIBUTIONS 79 5.5.1 CONTINUOUS ELLIPTICAL
DISTRIBUTIONS 80 5.5.2 TVAR FOR THE LINEAR EXPONENTIAL FAMILY 82 5.5.3
EXERCISE 84 5.6 EXTREME VALUE DISTRIBUTIONS 84 5.6.1 INTRODUCTION 84
5.6.2 DISTRIBUTION OF THE MAXIMUM 86 5.6.3 STABILITY OF THE MAXIMUM OF
THE EXTREME VALUE DISTRIBUTION 90 5.6.4 THE FISHER-TIPPETT THEOREM . 91
5.6.5 MAXIMUM DOMAIN OF ATTRACTION 93 5.6.6 GENERALIZED PARETO
DISTRIBUTIONS 95 5.6.7 STABILITY OF EXCESSES OF THE GENERALIZED PARETO
96 5.6.8 LIMITING DISTRIBUTIONS OF EXCESSES 98 5.6.9 TVAR FOR EXTREME
VALUE DISTRIBUTIONS 98 5.6.10 FURTHER READING 100 5.6.11 EXERCISES 100
DISCRETE DISTRIBUTIONS AND PROCESSES 101 6.1INTRODUCTION 101 6.1.1
EXERCISE 102 6.2 THE POISSON DISTRIBUTION 102 6.3 THE NEGATIVE BINOMIAL
DISTRIBUTION 105 6.4 THE BINOMIAL DISTRIBUTION 107 6.5 THE (A, B, 0)
CLASS 108 6.5.1 EXERCISES 111 6.6 COUNTING PROCESSES 111 6.6.1
INTRODUCTION AND DEFINITIONS 111 6.6.2 POISSON PROCESSES 114 6.6.3
PROCESSES WITH CONTAGION 116 6.6.4 OTHER PROCESSES 119 6.6.5 EXERCISES
120 6.7 TRUNCATION AND MODIFICATION AT ZERO 121 6.7.1 EXERCISES 126 6.8
COMPOUND FREQUENCY MODELS 126 6.8.1 EXERCISES 132 6.9 FURTHER PROPERTIES
OF THE COMPOUND POISSON CLASS 132 6.9.1 EXERCISES 137 6.10 MIXED
FREQUENCY DISTRIBUTIONS 137 6.10.1 GENERAL MIXED FREQUENCY DISTRIBUTION
137 6.10.2 MIXED POISSON DISTRIBUTIONS 139 6.10.3 EXERCISES 144 VIII
CONTENTS 6.11 MIXED POISSON PROCESSES 145 6.11.1 EXERCISES 149 6.12
EFFECT OF EXPOSURE ON FREQUENCY 151 6.13 AN INVENTORY OF DISCRETE
DISTRIBUTIONS 152 6.13.1 EXERCISES 152 6.14 TVAR FOR DISCRETE
DISTRIBUTIONS 155 6.14.1 TVAR FOR THE DISCRETE LINEAR EXPONENTIAL FAMILY
156 6.14.2 EXERCISES 159 161 161 162 163 164 164 165 166 171 171 173 174
176 177 FREQUENCY AND SEVERITY WITH COVERAGE MODIFICATIONS 179 8.1
INTRODUCTION 179 8.2 DEDUCTIBLES 179 8.2.1 EXERCISES 184 8.3 THE LOSS
ELIMINATION RATIO AND THE EFFECT OF INFLATION FOR ORDINARY DEDUCTIBLES
185 8.3.1 EXERCISES 186 8.4 POLICY LIMITS 187 8.4.1 EXERCISES 189 8.5
COINSURANCE, DEDUCTIBLES, AND LIMITS 189 8.5.1 EXERCISES 191 8.6 THE
IMPACT OF DEDUCTIBLES ON CLAIM FREQUENCY 192 8.6.1 EXERCISES 196
AGGREGATE LOSS MODELS 199 9.1 INTRODUCTION 199 9.1.1 EXERCISES 202 7
MULTIVARIATE MODELS 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 INTRODUCTION SKLAR S
THEOREM AND COPULAS MEASURES OF DEPENDENCY 7.3.1 SPEARMAN S RHO 7.3.2
KENDALL S TAU TAIL DEPENDENCE ARCHIMEDEAN COPULAS 7.5.1 EXERCISE
ELLIPTICAL COPULAS 7.6.1 EXERCISE EXTREME VALUE COPULAS 7.7.1 EXERCISES
ARCHIMAX COPULAS CONTENTS IX 9.2 MODEL CHOICES 202 9.2.1 EXERCISES 203
9.3 THE COMPOUND MODEL FOR AGGREGATE CLAIMS 203 9.3.1 EXERCISES 211 9.4
ANALYTIC RESULTS 217 9.4.1 EXERCISES 223 9.5 COMPUTING THE AGGREGATE
CLAIMS DISTRIBUTION 225 9.6 THE RECURSIVE METHOD 227 9.6.1 APPLICATIONS
TO COMPOUND FREQUENCY MODELS 228 9.6.2 UNDERFLOW/OVERFLOW PROBLEMS 230
9.6.3 NUMERICAL STABILITY 230 9.6.4 CONTINUOUS SEVERITY 231 9.6.5
CONSTRUCTING ARITHMETIC DISTRIBUTIONS 231 9.6.6 EXERCISES 234 9.7 THE
IMPACT OF INDIVIDUAL POLICY MODIFICATIONS ON AGGREGATE PAYMENTS 238
9.7.1 EXERCISES 241 9.8 INVERSION METHODS 241 9.8.1 FAST FOURIER
TRANSFORM 242 9.8.2 DIRECT NUMERICAL INVERSION 244 9.8.3 EXERCISE 246
9.9 CALCULATIONS WITH APPROXIMATE DISTRIBUTIONS 246 9.9.1 ARITHMETIC
DISTRIBUTIONS 246 9.9.2 EMPIRICAL DISTRIBUTIONS 249 9.9.3 PIECEWISE
LINEAR CDF 250 9.9.4 EXERCISES 251 9.10 COMPARISON OF METHODS 252 9.11
THE INDIVIDUAL RISK MODEL 253 9.11.1 THE MODEL 253 9.11.2 PARAMETRIC
APPROXIMATION 255 9.11.3 COMPOUND POISSON APPROXIMATION 256 9.11.4
EXERCISES 259 9.12 TVAR FOR AGGREGATE LOSSES 261 9.12.1 TVAR FOR
DISCRETE AGGREGATE LOSS DISTRIBUTIONS 262 9.12.2 AGGREGATE TVAR FOR SOME
FREQUENCY DISTRIBUTIONS 262 9.12.3 AGGREGATE TVAR FOR SOME SEVERITY
DISTRIBUTIONS 264 9.12.4 SUMMARY 267 9.12.5 EXERCISES 268 10
DISCRETE-TIME RUIN MODELS 269 10.1 INTRODUCTION 269 10.2 PROCESS MODELS
FOR INSURANCE 270 10.2.1 PROCESSES 270 X CONTENTS 10.2.2 AN INSURANCE
MODEL 271 10.2.3 RUIN 272 10.3 DISCRETE, FINITE-TIME RUIN PROBABILITIES
273 10.3.1 THE DISCRETE-TIME PROCESS 273 10.3.2 EVALUATING THE
PROBABILITY OF RUIN 274 10.3.3 EXERCISES 276 11 CONTINUOUS-TIME RUIN
MODELS 277 11.1 INTRODUCTION 277 11.1.1 THE POISSON PROCESS - 277 11.1.2
THE CONTINUOUS-TIME PROBLEM 278 11.2 THE ADJUSTMENT COEFFICIENT AND
LUNDBERG S INEQUALITY 279 11.2.1 THE ADJUSTMENT COEFFICIENT 279 11.2.2
LUNDBERG S INEQUALITY 283 11.2.3 EXERCISES 284 11.3 AN
INTEGRODIFFERENTIAL EQUATION 286 11.3.1 EXERCISES 290 11.4 THE MAXIMUM
AGGREGATE LOSS 291 11.4.1 EXERCISES 294 11.5 CRAMER S ASYMPTOTIC RUIN
FORMULA AND TIJMS APPROXIMATION 295 11.5.1 EXERCISES 300 11.6 THE
BROWNIAN MOTION RISK PROCESS 302 11.7 BROWNIAN MOTION AND THE
PROBABILITY OF RUIN 306 PART III CONSTRUCTION OF EMPIRICAL MODELS 12
REVIEW OF MATHEMATICAL STATISTICS 315 12.1 INTRODUCTION 315 12.2 POINT
ESTIMATION 316 12.2.1 INTRODUCTION 316 12.2.2 MEASURES OF QUALITY 317
12.2.3 EXERCISES 322 12.3 INTERVAL ESTIMATION 324 12.3.1 EXERCISES 326
12.4 TESTS OF HYPOTHESES 326 12.4.1 EXERCISE 330 13 ESTIMATION FOR
COMPLETE DATA 331 13.1 INTRODUCTION 331 13.2 THE EMPIRICAL DISTRIBUTION
FOR COMPLETE, INDIVIDUAL DATA * 335 13.2.1 EXERCISES 338 CONTENTS XI
13.3 EMPIRICAL DISTRIBUTIONS FOR GROUPED DATA 339 13.3.1 EXERCISES 341
14 ESTIMATION FOR MODIFIED DATA 343 14.1 POINT ESTIMATION 343 14.1.1
EXERCISES 349 14.2 MEANS, VARIANCES, AND INTERVAL ESTIMATION 351 14.2.1
EXERCISES 360 14.3 KERNEL DENSITY MODELS 362 14.3.1 EXERCISES 365 14.4
APPROXIMATIONS FOR LARGE DATA SETS 366 14.4.1 INTRODUCTION 366 14.4.2
KAPLAN-MEIER TYPE APPROXIMATIONS 367 14.4.3 EXERCISES 370 PART IV
PARAMETRIC STATISTICAL METHODS 15 PARAMETER ESTIMATION 375 15.1 METHOD
OF MOMENTS AND PERCENTILE MATCHING 375 15.1.1 EXERCISES 378 15.2 MAXIMUM
LIKELIHOOD ESTIMATION 381 15.2.1 INTRODUCTION 381 15.2.2 COMPLETE,
INDIVIDUAL DATA 383 15.2.3 COMPLETE, GROUPED DATA 384 15.2.4 TRUNCATED
OR CENSORED DATA 385 15.2.5 EXERCISES 388 15.3 VARIANCE AND INTERVAL
ESTIMATION 393 15.3.1 EXERCISES 399 15.4 NON-NORMAL CONFIDENCE INTERVALS
402 15.4.1 EXERCISE 404 15.5 BAYESIAN ESTIMATION 404 15.5.1 DEFINITIONS
AND BAYES THEOREM 404 15.5.2 INFERENCE AND PREDICTION 407 15.5.3
CONJUGATE PRIOR DISTRIBUTIONS AND THE LINEAR EXPONENTIAL FAMILY 414
15.5.4 COMPUTATIONAL ISSUES 415 15.5.5 EXERCISES 416 15.6 ESTIMATION FOR
DISCRETE DISTRIBUTIONS 422 15.6.1 POISSON 422 15.6.2 NEGATIVE BINOMIAL
425 15.6.3 BINOMIAL 427 15.6.4 THE (A, B, 1 ) CLASS 430 XII CONTENTS
15.6.5 COMPOUND MODELS 434 15.6.6 EFFECT OF EXPOSURE ON MAXIMUM
LIKELIHOOD ESTIMATION 435 15.6.7 EXERCISES 436 16 MODEL SELECTION 441
16.1 INTRODUCTION 441 16.2 REPRESENTATIONS OF THE DATA AND MODEL 442
16.3 GRAPHICAL COMPARISON OF THE DENSITY AND DISTRIBUTION FUNCTIONS 443
16.3.1 EXERCISES - 447 16.4 HYPOTHESIS TESTS 448 16.4.1
KOLMOGOROV-SMIRNOV TEST 448 16.4.2 ANDERSON-DARLING TEST 450 16.4.3
CHI-SQUARE GOODNESS-OF-FIT TEST 451 16.4.4 LIKELIHOOD RATIO TEST 455
16.4.5 EXERCISES 456 16.5 SELECTING A MODEL 459 16.5.1 INTRODUCTION 459
16.5.2 JUDGMENT-BASED APPROACHES 459 16.5.3 SCORE-BASED APPROACHES 460
16.5.4 EXERCISES 467 17 ESTIMATION AND MODEL SELECTION FOR MORE COMPLEX
MODELS 473 17.1 EXTREME VALUE MODELS 473 17.1.1 INTRODUCTION 473 17.1.2
PARAMETER ESTIMATION 474 17.2 COPULA MODELS 484 17.2.1 INTRODUCTION 484
17.2.2 MAXIMUM LIKELIHOOD ESTIMATION 484 17.2.3 SEMIPARAMETRIC
ESTIMATION OF THE COPULA 486 17.2.4 THE ROLE OF DEDUCTIBLES 487 17.2.5
GOODNESS-OF-FIT TESTING 489 17.2.6 AN EXAMPLE 490 17.2.7 EXERCISE 491
17.3 MODELS WITH COVARIATES 492 17.3.1 INTRODUCTION 492 17.3.2
PROPORTIONAL HAZARDS MODELS 493 17.3.3 THE GENERALIZED LINEAR AND
ACCELERATED FAILURE TIME MODELS 498 17.3.4 EXERCISES 501 CONTENTS XIII
18 FIVE EXAMPLES 503 18.1 INTRODUCTION 503 18.2 TIME TO DEATH 503 18.2.1
THE DATA 503 18.2.2 SOME CALCULATIONS 505 18.2.3 EXERCISE 506 18.3 TIME
FROM INCIDENCE TO REPORT 506 18.3.1 THE PROBLEM AND SOME DATA 507 18.3.2
ANALYSIS 507 18.4 PAYMENT AMOUNT 508 18.4.1 THE DATA 508 18.4.2 THE
FIRST MODEL 510 18.4.3 THE SECOND MODEL 512 18.5 AN AGGREGATE LOSS
EXAMPLE 512 18.6 ANOTHER AGGREGATE LOSS EXAMPLE 516 18.6.1 DISTRIBUTION
FOR A SINGLE POLICY 516 18.6.2 ONE HUNDRED POLICIES*EXCESS OF LOSS 516
18.6.3 ONE HUNDRED POLICIES*AGGREGATE STOP-LOSS 517 18.6.4 NUMERICAL
CONVOLUTIONS 519 18.7 COMPREHENSIVE EXERCISES 520 PART V ADJUSTED
ESTIMATES 19 INTERPOLATION AND SMOOTHING 527 19.1 INTRODUCTION 527 19.2
POLYNOMIAL INTERPOLATION AND SMOOTHING 529 19.2.1 EXERCISES 533 19.3
CUBIC SPLINE INTERPOLATION 533 19.3.1 CONSTRUCTION OF CUBIC SPLINES 534
19.3.2 EXERCISES 541 19.4 APPROXIMATING FUNCTIONS WITH SPLINES 542
19.4.1 EXERCISE 545 19.5 EXTRAPOLATING WITH SPLINES 546 19.5.1 EXERCISE
546 19.6 SMOOTHING SPLINES 546 19.6.1 EXERCISE 554 20 CREDIBILITY 555
20.1 INTRODUCTION 555 20.2 LIMITED FLUCTUATION CREDIBILITY THEORY 557
20.2.1 FULL CREDIBILITY 558 20.2.2 PARTIAL CREDIBILITY 561 XIV
CONTENTS 20.2.3 PROBLEMS WITH THE APPROACH 564 20.2.4 NOTES AND
REFERENCES 565 20.2.5 EXERCISES 565 20.3 GREATEST ACCURACY CREDIBILITY
THEORY 567 20.3.1 INTRODUCTION 567 20.3.2 CONDITIONAL DISTRIBUTIONS AND
EXPECTATION 570 20.3.3 THE BAYESIAN METHODOLOGY 573 20.3.4 THE
CREDIBILITY PREMIUM 581 20.3.5 THE BUHLMANN MODEL 584 20.3.6 THE
BUHLMANN-STRAUB MODEL 588 20.3.7 EXACT CREDIBILITY 593 20.3.8 LINEAR
VERSUS BAYESIAN VERSUS NO CREDIBILITY 597 20.3.9 NOTES AND REFERENCES
604 20.3.10 EXERCISES 604 20.4 EMPIRICAL BAYES PARAMETER ESTIMATION 617
20.4.1 NONPARAMETRIC ESTIMATION 620 20.4.2 SEMIPARAMETRIC ESTIMATION 630
20.4.3 PARAMETRIC ESTIMATION 632 20.4.4 NOTES AND REFERENCES 636 20.4.5
EXERCISES 637 PART VI SIMULATION 21 SIMULATION 643 21.1 B ASICS OF
SIMULATION 643 21.1.1 THE SIMULATION APPROACH 644 21.1.2 EXERCISES 649
21.2 EXAMPLES OF SIMULATION IN ACTUARIAL MODELING 649 21.2.1 AGGREGATE
LOSS CALCULATIONS 649 21.2.2 EXAMPLES OF LACK OF INDEPENDENCE OR
IDENTICAL DISTRIBUTIONS 650 21.2.3 SIMULATION ANALYSIS OF THE TWO
EXAMPLES 651 21.2.4 SIMULATING COPULAS 653 21.2.5 USING SIMULATION TO
DETERMINE RISK MEASURES 656 21.2.6 STATISTICAL ANALYSES 656 21.2.7
EXERCISES 658 21.3 EXAMPLES OF SIMULATION IN FINANCE 660 21.3.1
INVESTMENT GUARANTEES 661 21.3.2 OPTION VALUATION 662 21.3.3 EXERCISE
664 CONTENTS XV APPENDIX A: AN INVENTORY OF CONTINUOUS DISTRIBUTIONS 665
A. 1 INTRODUCTION 665 A.2 TRANSFORMED BETA FAMILY 669 A.2.1
FOUR-PARAMETER DISTRIBUTION 669 A.2.2 THREE-PARAMETER DISTRIBUTIONS 669
A.2.3 TWO-PARAMETER DISTRIBUTIONS 671 A.3 TRANSFORMED GAMMA FAMILY 673
A.3.1 THREE-PARAMETER DISTRIBUTIONS 673 A.3.2 TWO-PARAMETER
DISTRIBUTIONS 674 A.3.3 ONE-PARAMETER DISTRIBUTIONS 676 A.4
DISTRIBUTIONS FOR LARGE LOSSES 677 A.4.1 EXTREME VALUE DISTRIBUTIONS 677
A.4.2 GENERALIZED PARETO DISTRIBUTIONS 678 A.5 OTHER DISTRIBUTIONS 678
A.6 DISTRIBUTIONS WITH FINITE SUPPORT 680 APPENDIX B: AN INVENTORY OF
DISCRETE DISTRIBUTIONS 683 B.I INTRODUCTION 683 B.2 THE (A, B, 0) CLASS
684 B.3 THE (A, B, 1) CLASS 685 B.3.1 THE ZERO-TRUNCATED SUBCLASS 685
B.3.2 THE ZERO-MODIFIED SUBCLASS 687 B.4 THE COMPOUND CLASS 688 B.4.1
SOME COMPOUND DISTRIBUTIONS 688 B.5 A HIERARCHY OF DISCRETE
DISTRIBUTIONS 690 APPENDIX C: FREQUENCY AND SEVERITY RELATIONSHIPS 691
APPENDIX D: THE RECURSIVE FORMULA 693 APPENDIX E: DISCRETIZATION OF THE
SEVERITY DISTRIBUTION 695 E. 1 THE METHOD OF ROUNDING 695 E.2 MEAN
PRESERVING 696 E.3 UNDISCRETIZATION OF A DISCRETIZED DISTRIBUTION 696
APPENDIX F: NUMERICAL OPTIMIZATION AND SOLUTION OF SYSTEMS OF EQUATIONS
699 F.I MAXIMIZATION USING SOLVER 699 F.2 THE SIMPLEX METHOD 704 F.3
USING EXCEL TO SOLVE EQUATIONS 705 REFERENCES 709 INDEX 719
|
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| author | Klugman, Stuart A. 1949- Panjer, Harry H. 1946- Willmot, Gordon E. 1957- |
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| edition | 3. ed. |
| format | Book |
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| genre | (DE-588)4143389-0 Aufgabensammlung gnd-content |
| genre_facet | Aufgabensammlung |
| id | DE-604.BV035860547 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:06:21Z |
| institution | BVB |
| isbn | 9780470187814 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018718415 |
| oclc_num | 229464685 |
| open_access_boolean | |
| owner | DE-945 DE-91G DE-BY-TUM DE-11 DE-355 DE-BY-UBR |
| owner_facet | DE-945 DE-91G DE-BY-TUM DE-11 DE-355 DE-BY-UBR |
| physical | XIX, 726 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Klugman, Stuart A. 1949- Verfasser (DE-588)1044735155 aut Loss models from data to decisions Stuart A. Klugman ; Harry H. Panjer ; Gordon E. Willmot 3. ed. Hoboken, NJ Wiley 2008 XIX, 726 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Includes bibliographical references Assurance - Mathématiques Assurance - Modèles mathématiques Assurance - Méthodes statistiques Mathematik Insurance / Mathematics Insurance, Life / Mathematics Risikotheorie (DE-588)4135592-1 gnd rswk-swf Versicherungsmathematik (DE-588)4063194-1 gnd rswk-swf Verlustrechnung (DE-588)4187883-8 gnd rswk-swf Versicherungsstatistik (DE-588)4235273-3 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Versicherungsmathematik (DE-588)4063194-1 s Verlustrechnung (DE-588)4187883-8 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Risikotheorie (DE-588)4135592-1 s Versicherungsstatistik (DE-588)4235273-3 s 1\p DE-604 Panjer, Harry H. 1946- Verfasser (DE-588)1044735732 aut Willmot, Gordon E. 1957- Verfasser (DE-588)122585860 aut DE-576;wiley image/jpeg http://swbplus.bsz-bw.de/bsz288467795cov.htm 20090320114443 Cover GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018718415&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Klugman, Stuart A. 1949- Panjer, Harry H. 1946- Willmot, Gordon E. 1957- Loss models from data to decisions Assurance - Mathématiques Assurance - Modèles mathématiques Assurance - Méthodes statistiques Mathematik Insurance / Mathematics Insurance, Life / Mathematics Risikotheorie (DE-588)4135592-1 gnd Versicherungsmathematik (DE-588)4063194-1 gnd Verlustrechnung (DE-588)4187883-8 gnd Versicherungsstatistik (DE-588)4235273-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4135592-1 (DE-588)4063194-1 (DE-588)4187883-8 (DE-588)4235273-3 (DE-588)4114528-8 (DE-588)4143389-0 |
| title | Loss models from data to decisions |
| title_auth | Loss models from data to decisions |
| title_exact_search | Loss models from data to decisions |
| title_full | Loss models from data to decisions Stuart A. Klugman ; Harry H. Panjer ; Gordon E. Willmot |
| title_fullStr | Loss models from data to decisions Stuart A. Klugman ; Harry H. Panjer ; Gordon E. Willmot |
| title_full_unstemmed | Loss models from data to decisions Stuart A. Klugman ; Harry H. Panjer ; Gordon E. Willmot |
| title_short | Loss models |
| title_sort | loss models from data to decisions |
| title_sub | from data to decisions |
| topic | Assurance - Mathématiques Assurance - Modèles mathématiques Assurance - Méthodes statistiques Mathematik Insurance / Mathematics Insurance, Life / Mathematics Risikotheorie (DE-588)4135592-1 gnd Versicherungsmathematik (DE-588)4063194-1 gnd Verlustrechnung (DE-588)4187883-8 gnd Versicherungsstatistik (DE-588)4235273-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Assurance - Mathématiques Assurance - Modèles mathématiques Assurance - Méthodes statistiques Mathematik Insurance / Mathematics Insurance, Life / Mathematics Risikotheorie Versicherungsmathematik Verlustrechnung Versicherungsstatistik Mathematisches Modell Aufgabensammlung |
| url | http://swbplus.bsz-bw.de/bsz288467795cov.htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018718415&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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