Loss Models (5th Ed.)
From Data to Decisions

Wiley Series in Probability and Statistics Series

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Language: Anglais
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560 p. · Hardback

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.

Preface xiii
About the Companion Website xv

Part I Introduction
1 Modeling 3
2 Random Variables 9
3 Basic Distributional Quantities 21

Part II Actuarial Models
4 Characteristics of Actuarial Models 51
5 Continuous Models 61
6 Discrete Distributions 81
7 Advanced Discrete Distributions 99
8 Frequency and Severity with Coverage Modifications 125
9 Aggregate Loss Models 147

Part III Mathematical Statistics
10 Introduction to Mathematical Statistics 201
11 Maximum Likelihood Estimation 229
12 Frequentist Estimation for Discrete Distributions 255
13 Bayesian Estimation 275

Part IV Construction of Models
14 Construction of Empirical Models 295
15 Model Selection 353

Part V Credibility
16 Introduction to Limited Fluctuation Credibility 387
17 Greatest Accuracy Credibility 401
18 Empirical Bayes Parameter Estimation 445

Part VI Simulation 19 Simulation 467

A An Inventory of Continuous Distributions 489
A.1 Introduction 489
A.2 The Transformed Beta Family 493
A.2.1 The Four-Parameter Distribution 493
A.2.2 Three-Parameter Distributions 493
A.2.3 Two-Parameter Distributions 494
A.3 The Transformed Gamma Family 496
A.3.1 Three-Parameter Distributions 496
A.3.2 Two-Parameter Distributions 497
A.3.3 One-Parameter Distributions 499
A.4 Distributions for Large Losses 499
A.4.1 Extreme Value Distributions 499
A.4.2 Generalized Pareto Distributions 500
A.5 Other Distributions 501
A.6 Distributions with Finite Support 502
B An Inventory of Discrete Distributions 505
B.1 Introduction 505
B.2 The (a, b, 0) Class 506
B.3 The (a, b, 1) Class 507
B.3.1 The Zero-Truncated Subclass 507
B.3.2 The Zero-Modified Subclass 509
B.4 The Compound Class 509
B.4.1 Some Compound Distributions 510
B.5 A Hierarchy of Discrete Distributions 511
C Frequency and Severity Relationships 513
D The Recursive Formula 515
E Discretization of the Severity Distribution 517
E.1 The Method of Rounding 517
E.2 Mean Preserving 518
E.3 Undiscretization of a Discretized Distribution 518
References 521
Index 529