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A guide that provides in-depth coverage of modeling techniques used throughout many branches of actuarial science, revised and updated Now in its fifth edition, Loss Models: From Data to Decisions puts the focus on material tested in the Society of Actuaries (SOA) newly revised Exams STAM (Short-Term Actuarial Mathematics) and LTAM (Long-Term Actuarial Mathematics). Updated to reflect these exam changes, this vital resource offers actuaries, and those aspiring to the profession, a practical approach to the concepts and techniques needed to succeed in the profession. The techniques are also valuable for anyone who uses loss data to build models for assessing risks of any kind. Loss Models contains a wealth of examples that highlight the real-world applications of the concepts presented, and puts the emphasis on calculations and spreadsheet implementation. With a focus on the loss process, the book reviews the essential quantitative techniques such as random variables, basic distributional quantities, and the recursive method, and discusses techniques for classifying and creating distributions. Parametric, non-parametric, and Bayesian estimation methods are thoroughly covered. In addition, the authors offer practical advice for choosing an appropriate model. This important text: Presents a revised and updated edition of the classic guide for actuaries that aligns with newly introduced Exams STAM and LTAM Contains a wealth of exercises taken from previous exams Includes fresh and additional content related to the material required by the Society of Actuaries (SOA) and the Canadian Institute of Actuaries (CIA) Offers a solutions manual available for further insight, and all the data sets and supplemental material are posted on a companion site Written for students and aspiring actuaries who are preparing to take the SOA examinations, Loss Models offers an essential guide to the concepts and techniques of actuarial science.
Autorentext
STUART A. KLUGMAN, PHD, FSA, CERA, is Staff Fellow (Education) at the Society of Actuaries (SOA) and Principal Financial Group Distinguished Professor Emeritus of Actuarial Science at Drake University. He has served as SOA vice president. HARRY H. PANJER, PHD, FSA, FCIA, CERA, HonFIA, is Distinguished Professor Emeritus in the Department of Statistics and Actuarial Science at the University of Waterloo, Canada. He has served as CIA president and as SOA president. GORDON E. WILLMOT, PHD, FSA, FCIA, is Munich Re Chair in Insurance and Professor in the Department of Statistics and Actuarial Science at the University of Waterloo, Canada.
Klappentext
A GUIDE THAT PROVIDES IN-DEPTH COVERAGE OF MODELING TECHNIQUES USED THROUGHOUT MANY BRANCHES OF ACTUARIAL SCIENCE, REVISED AND UPDATED Now in its fifth edition, Loss Models: From Data to Decisions puts the focus on material tested in the Society of Actuaries' newly revised Exams STAM (Short-Term Actuarial Mathematics) and LTAM (Long-Term Actuarial Mathematics). Updated to reflect these exam changes, this vital resource offers actuaries, and those aspiring to the profession, a practical approach to the concepts and techniques needed to succeed in the profession. The techniques are also valuable for anyone who uses loss data to build models for assessing risks of any kind. Loss Models contains a wealth of examples that highlight the real-world applications of the concepts presented, and puts the emphasis on calculations and spreadsheet implementation. With a focus on the loss process, the book reviews the essential quantitative techniques such as random variables, basic distributional quantities, and the recursive method, and discusses techniques for classifying and creating distributions. Parametric, non-parametric, and Bayesian estimation methods are thoroughly covered. In addition, the authors offer practical advice for choosing an appropriate model. This important text:
Inhalt
Preface xiii
About the Companion Website xv
Part I Introduction
1 Modeling 3
1.1 The Model-Based Approach 3
1.1.1 The Modeling Process 3
1.1.2 The Modeling Advantage 5
1.2 The Organization of This Book 6
2 Random Variables 9
2.1 Introduction 9
2.2 Key Functions and Four Models 11
2.2.1 Exercises 19
3 Basic Distributional Quantities 21
3.1 Moments 21
3.1.1 Exercises 28
3.2 Percentiles 29
3.2.1 Exercises 31
3.3 Generating Functions and Sums of Random Variables 31
3.3.1 Exercises 33
3.4 Tails of Distributions 33
3.4.1 Classification Based on Moments 33
3.4.2 Comparison Based on Limiting Tail Behavior 34
3.4.3 Classification Based on the Hazard Rate Function 35
3.4.4 Classification Based on the Mean Excess Loss Function 36
3.4.5 Equilibrium Distributions and Tail Behavior 38
3.4.6 Exercises 39
3.5 Measures of Risk 41
3.5.1 Introduction 41
3.5.2 Risk Measures and Coherence 41
3.5.3 Value at Risk 43
3.5.4 Tail Value at Risk 44
3.5.5 Exercises 48
Part II Actuarial Models
4 Characteristics of Actuarial Models 51
4.1 Introduction 51
4.2 The Role of Parameters 51
4.2.1 Parametric and Scale Distributions 52
4.2.2 Parametric Distribution Families 54
4.2.3 Finite Mixture Distributions 54
4.2.4 Data-Dependent Distributions 56
4.2.5 Exercises 59
5 Continuous Models 61
5.1 Introduction 61
5.2 Creating New Distributions 61
5.2.1 Multiplication by a Constant 62
5.2.2 Raising to a Power 62
5.2.3 Exponentiation 64
5.2.4 Mixing 64
5.2.5 Frailty Models 68
5.2.6 Splicing 69
5.2.7 Exercises 70
5.3 Selected Distributions and Their Relationships 74
5.3.1 Introduction 74
5.3.2 Two Parametric Families 74
5.3.3 Limiting Distributions 74
5.3.4 Two Heavy-Tailed Distributions 76
5.3.5 Exercises 77
5.4 The Linear Exponential Family 78
5.4.1 Exercises 80
6 Discrete Distributions 81
6.1 Introduction 81
6.1.1 Exercise 82
6.2 The Poisson Distribution 82
6.3 The Negative Binomial Distribution 85
6.4 The Binomial Distribution 87
6.5 The (𝑎, 𝑏, 0) Class 88
6.5.1 Exercises 91
6.6 Truncation and Modification at Zero 92
6.6.1 Exercises 96
7 Advanced Discrete Distributions 99
7.1 Compound Frequency Distributions 99
7.1.1 Exercises 105
7.2 Further Properties of the Compound Poisson Class 105
7.2.1 Exercises 111
7.3 Mixed-Frequency Distributions 111
7.3.1 The General Mixed-Frequency Distribution 111
7.3.2 Mixed Poisson Distributions 113
7.3.3 Exercises 118
7.4 The Effect of Exposure on Frequency 120
7.5 An Inventory of Discrete Distributions 121
7.5.1 Exercises 122
8 Frequency and Severity with Coverage Modifications 125
8.1 Introduction 125
8.2 Deductibles 126
8.2.1 Exercises 131
8.3 The Loss Elimination Ratio and the Effect of Inflation for Ordinary Deductibles 132
8.3.1 Exercises 133
8.4 Policy Limits 134
8.4.1 Exercises 136
8.5 Coinsurance, Deductibles, and Limits 136
8.5.1 Exercises 138
8.6 The Impact of Deductibles on Claim Frequency 140
8.6.1 Exercises 144
9 Aggregate Loss Models 147
9.1 Introduction 147
9.1.1 Exercises 150 ...