Holdings: Loss models :: THWS Bibkatalog

Loss models: from data to decisions

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Bibliographic Details
Main Authors:	Klugman, Stuart A. 1949- (Author), Panjer, Harry H. 1946- (Author), Willmot, Gordon E. 1957- (Author)
Format:	Book
Language:	English
Published:	Hoboken, NJ Wiley 2008
Edition:	3. ed.
Series:	Wiley series in probability and statistics
Subjects:	Assurance - Mathématiques Assurance - Modèles mathématiques Assurance - Méthodes statistiques Mathematik Insurance / Mathematics Insurance, Life / Mathematics Risikotheorie Versicherungsmathematik Verlustrechnung Versicherungsstatistik Mathematisches Modell Aufgabensammlung
Online Access:	Cover Inhaltsverzeichnis
Item Description:	Includes bibliographical references
Physical Description:	XIX, 726 S. graph. Darst.
ISBN:	9780470187814

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_version_	1804140839341916160
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 POLICIESEXCESS OF LOSS 516 18.6.3 ONE HUNDRED POLICIESAGGREGATE 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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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
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physical	XIX, 726 S. graph. Darst.
publishDate	2008
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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
work_keys_str_mv	AT klugmanstuarta lossmodelsfromdatatodecisions AT panjerharryh lossmodelsfromdatatodecisions AT willmotgordone lossmodelsfromdatatodecisions

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