Predictive modeling applications in actuarial science: Volume 1 Predictive modeling techniques
Gespeichert in:
| Weitere Verfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Cambridge Univ. Press
2014
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| Ausgabe: | First published |
| Schriftenreihe: | International series on actuarial science
International series on actuarial science |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xx, 543 Seiten Diagramme |
| ISBN: | 9781107029873 |
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| 245 | 1 | 0 | |a Predictive modeling applications in actuarial science |n Volume 1 |p Predictive modeling techniques |c [edited by] Edward W. Frees, University of Wisconsin, Madison, Richard A. Derrig, Opal Consulting LLC, Glenn Meyers, ISO Innovative Analytics, Jersey City, New Jersey |
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Datensatz im Suchindex
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| adam_text | Titel: Bd. 1. Predictive modeling applications in actuarial science. Predictive modeling techniques
Autor:
Jahr: 2014
Contents
Contributor List page xiii
Acknowledgments xix
1 Predictive Modeling in Actuarial Science 1
Edward W. Frees, Richard A. Derrig, and Glenn Meyers
1.1 Introduction 1
1.2 Predictive Modeling and Insurance Company Operations 3
1.3 A Short History of Predictive Modeling in Actuarial Science 5
1.4 Goals of the Series 8
References 9
I Predictive Modeling Foundations
2 Overview of Linear Models 13
Marjorie Rosenberg and James Guszcza
2.1 Introduction 13
2.2 Linear Model Theory with Examples 15
2.3 Case Study 45
2.4 Conclusion 59
2.5 Exercises 60
References 63
3 Regression with Categorical Dependent Variables 65
Montserrat Guillen
3.1 Coding Categorical Variables 65
3.2 Modeling a Binary Response 66
3.3 Logistic Regression Model 67
3.4 Probit and Other Binary Regression Models 78
3.5 Models for Ordinal Categorical Dependent Variables 79
3.6 Models for Nominal Categorical Dependent Variables 81
3.7 Further Reading 85
References 86
4 Regression with Count-Dependent Variables 87
Jean-Philippe Boucher
4.1 Introduction 87
4.2 Poisson Distribution 87
4.3 Poisson Regression 89
4.4 Heterogeneity in the Distribution 92
4.5 Zero-Inflated Distribution 102
4.6 Conclusion 105
4.7 Further Reading 105
References 105
5 Generalized Linear Models 107
Curtis Gary Dean
5.1 Introduction to Generalized Linear Models 107
5.2 Exponential Family of Distributions 110
5.3 Link Functions 115
5.4 Maximum Likelihood Estimation 118
5.5 Generalized Linear Model Review 121
5.6 Applications 122
5.7 Comparing Models 129
5.8 Conclusion 133
5.9 Appendix A. Binomial and Gamma Distributions in
Exponential Family Form 133
5.10 Appendix B. Calculating Mean and Variance from
Exponential Family Form 135
References 136
6 Frequency and Severity Models 138
Edward W. Frees
6.1 How Frequency Augments Severity Information 138
6.2 Sampling and the Generalized Linear Model 140
6.3 Frequency-Severity Models 148
6.4 Application: Massachusetts Automobile Claims 152
6.5 Further Reading 160
6.6 Appendix A. Sample Average Distribution in Linear
Exponential Families 161
6.7 Appendix B. Over-Sampling Claims 162
References 164
II Predictive Modeling Methods
7 Longitudinal and Panel Data Models 167
Edward W. Frees
7.1 Introduction 167
7.2 Linear Models 172
7.3 Nonlinear Models 176
7.4 Additional Considerations 180
7.5 Further Reading 181
References 181
8 Linear Mixed Models 182
Katrien Antonio and Yanwei Zhang
8.1 Mixed Models in Actuarial Science 182
8.2 Linear Mixed Models 192
8.3 Examples 201
8.4 Further Reading and Illustrations 213
References 215
9 Credibility and Regression Modeling 217
Vytaras Brazauskas, Harald Dornheim, and Ponmalar Ratnam
9.1 Introduction 217
9.2 Credibility and the LMM Framework 220
9.3 Numerical Examples 224
9.4 Theory versus Practice 227
9.5 Further Reading 232
9.6 Appendix 233
References 234
10 Fat-Tailed Regression Models 236
Peng Shi
10.1 Introduction 236
10.2 Transformation 238
10.3 GLM 241
10.4 Regression with Generalized Distributions 243
10.5 Median Regression 250
10.6 Appendix A. Tail Measure 255
10.7 Appendix B. Information Matrix for GB2 Regression 256
References 258
11 Spatial Modeling 260
Eike Brechmann and Claudia Czado
11.1 Introduction 260
11.2 Exploratory Analysis of Spatial Data 262
11.3 Spatial Autoregression 265
11.4 Average Claim Size Modeling 269
11.5 Hierarchical Model for Total Loss 273
11.6 Discussion and Conclusion 278
References 278
12 Unsupervised Learning 280
Louise Francis
12.1 Introduction 280
12.2 Datasets 283
12.3 Factor and Principal Components Analysis 285
12.4 Cluster Analysis 294
12.5 Exercises 309
References 310
III Bayesian and Mixed Modeling
13 Bayesian Computational Methods 315
Brian Hartman
13.1 Why Bayesian? 315
13.2 Personal Automobile Claims Modeling 316
13.3 Basics of Bayesian Statistics 316
13.4 Computational Methods 319
13.5 Prior Distributions 326
13.6 Conclusion 330
13.7 Further Reading 330
References 331
14 Bayesian Regression Models 334
Luis E. Nieto-Barajas and Enrique de Alba
14.1 Introduction 334
14.2 The Bayesian Paradigm 335
14.3 Generalized Linear Models 338
14.4 Mixed and Hierarchical Models 354
14.5 Nonparametric Regression 358
14.6 Appendix. Formal Definition of a Polya Tree 362
References 365
15 Generalized Additive Models and Nonparametric Regression 367
Patrick L. Brockett, Shuo-Li Chuang, and Utai Pitaktong
15.1 Motivation for Generalized Additive Models and
Nonparametric Regression 367
15.2 Additive Models for Nonparametric Regression 370
15.3 The Generalized Additive Model 388
15.4 Conclusion 395
References 396
16 Nonlinear Mixed Models 398
Katrien Antonio and Yanwei Zhang
16.1 Introduction 398
16.2 Model Families for Multilevel Non-Gaussian Data 399
16.3 Generalized Linear Mixed Models 399
16.4 Nonlinear Mixed Models 411
16.5 Bayesian Approach to (L,GL,NL)MMs 411
16.6 Example: Poisson Regression for Workers
Compensation Insurance Frequencies 412
References 423
IV Longitudinal Modeling
17 Time Series Analysis 427
Piet de Jong
17.1 Exploring Time Series Data 427
17.2 Modeling Foundations 431
17.3 Autoregressive, Moving Average (ARMA) Models 434
17.4 Additional Time Series Models 443
17.5 Further Reading 448
References 448
18 Claims Triangles/Loss Reserves 449
Greg Taylor
18.1 Introduction to Loss Reserving 449
18.2 The Chain Ladder 453
18.3 Models of Aggregate Claims Triangles 455
18.4 Models of Individual Claims 467
References 479
19 Survival Models 481
Jim Robinson
19.1 Survival Distribution Notation 481
19.2 Survival Data Censoring and Truncation 482
19.3 National Nursing Home Survey 482
19.4 Nonparametric Estimation of the Survival Function 486
19.5 Proportional Hazards Model 497
19.6 Parametric Survival Modeling 507
19.7 Further Reading 51!
19.8 Exercises 511
19.9 Appendix. National Nursing Home Survey Data 513
References 514
20 Transition Modeling 515
Bruce Jones and Weijia Wu
20.1 Multistate Models and Their Actuarial Applications 516
20.2 Describing a Multistate Model 518
20.3 Estimating the Transition Intensity Functions 522
20.4 Estimating the Transition Intensities with Outcomes
Observed at Distinct Time Points 534
References 536
Index 539
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| spelling | Predictive modeling applications in actuarial science Volume 1 Predictive modeling techniques [edited by] Edward W. Frees, University of Wisconsin, Madison, Richard A. Derrig, Opal Consulting LLC, Glenn Meyers, ISO Innovative Analytics, Jersey City, New Jersey First published New York, NY Cambridge Univ. Press 2014 xx, 543 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier International series on actuarial science Prognoseverfahren (DE-588)4358095-6 gnd rswk-swf Versicherungswissenschaft (DE-588)4188017-1 gnd rswk-swf Prognose (DE-588)4047390-9 gnd rswk-swf Mathematische Modellierung (DE-588)7651795-0 gnd rswk-swf Versicherungsmathematik (DE-588)4063194-1 gnd rswk-swf Versicherungswissenschaft (DE-588)4188017-1 s Versicherungsmathematik (DE-588)4063194-1 s Prognoseverfahren (DE-588)4358095-6 s Prognose (DE-588)4047390-9 s Mathematische Modellierung (DE-588)7651795-0 s DE-604 Frees, Edward W. 1953- (DE-588)132284375 edt Derrig, Richard A. (DE-588)171729250 edt Meyers, Glenn (DE-588)1064600190 edt (DE-604)BV042152739 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027688668&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Predictive modeling applications in actuarial science Prognoseverfahren (DE-588)4358095-6 gnd Versicherungswissenschaft (DE-588)4188017-1 gnd Prognose (DE-588)4047390-9 gnd Mathematische Modellierung (DE-588)7651795-0 gnd Versicherungsmathematik (DE-588)4063194-1 gnd |
| subject_GND | (DE-588)4358095-6 (DE-588)4188017-1 (DE-588)4047390-9 (DE-588)7651795-0 (DE-588)4063194-1 |
| title | Predictive modeling applications in actuarial science |
| title_auth | Predictive modeling applications in actuarial science |
| title_exact_search | Predictive modeling applications in actuarial science |
| title_full | Predictive modeling applications in actuarial science Volume 1 Predictive modeling techniques [edited by] Edward W. Frees, University of Wisconsin, Madison, Richard A. Derrig, Opal Consulting LLC, Glenn Meyers, ISO Innovative Analytics, Jersey City, New Jersey |
| title_fullStr | Predictive modeling applications in actuarial science Volume 1 Predictive modeling techniques [edited by] Edward W. Frees, University of Wisconsin, Madison, Richard A. Derrig, Opal Consulting LLC, Glenn Meyers, ISO Innovative Analytics, Jersey City, New Jersey |
| title_full_unstemmed | Predictive modeling applications in actuarial science Volume 1 Predictive modeling techniques [edited by] Edward W. Frees, University of Wisconsin, Madison, Richard A. Derrig, Opal Consulting LLC, Glenn Meyers, ISO Innovative Analytics, Jersey City, New Jersey |
| title_short | Predictive modeling applications in actuarial science |
| title_sort | predictive modeling applications in actuarial science predictive modeling techniques |
| topic | Prognoseverfahren (DE-588)4358095-6 gnd Versicherungswissenschaft (DE-588)4188017-1 gnd Prognose (DE-588)4047390-9 gnd Mathematische Modellierung (DE-588)7651795-0 gnd Versicherungsmathematik (DE-588)4063194-1 gnd |
| topic_facet | Prognoseverfahren Versicherungswissenschaft Prognose Mathematische Modellierung Versicherungsmathematik |
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