Initiation à l’algorithmique - 135 exercices corrigés

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. Content: Intro Copyright Page LOSS MODELS CONTENTS PREFACE ABOUT THE COMPANION WEBSITE PART I INTRODUCTION 1. MODELING The Model-Based ApproachThe 1.1.1 The Modeling The Modeling Advantage The Organization of This Book 2. RANDOM VARIABLES 2.1 Introduction 2.2 Key Functions and Four Models 2.2.1 Exercises 3. BASIC DISTRIBUTIONAL QUANTITIES 3.1 Moments 3.1.1 Exercises 3.2 Percentiles 3.2.1 Exercises 3.3 Generating Functions and Sums of Random Variables 3.3.1 Exercises 3.4 Tails of Distributions 3.4.1 Classification Based on Moments 3.4.2 Comparison Based on Limiting Tail 3.4.3 Classification Based on the Hazard Rate Function3.4.4 Classification Based on the Mean Excess Loss Function The mean excess 3.4.5 Equilibrium Distributions and Tail Behavior 3.4.6 Exercises 3.5 Measures of Risk 3.5.1 Introduction 3.5.2 Risk Measures and Coherence 3.5.3 Value at Risk 3.5.4 Tail Value of Risk 3.5.5 Exercises PART II ACTUARIAL MODELS 4. CHARACTERISTICS OF ACTUARIALMODELS 4.1 Introduction 4.2 The Role of Parameters 4.2.1 Parametric and Scale Distributions 4.2.2 Parametric Distribution Families 4.2.3 Finite Mixture Distributions 4.2.4 Data-Dependent Distributions4.2.5 Exercises 5. CONTINUOUS MODELS 5.1 Introduction 5.2 Creating New Distributions 5.2.1 Multiplication by a Constant 5.2.2 Raising to a Power 5.2.3 Exponentiation 5.2.4 Mixing 5.2.5 Frailty Models 5.2.6 Splicing 5.2.7 Exercises 5.3 Selected Distributions and Their Relationships 5.3.1 Introduction 5.3.2 Two Parametric Families 5.3.3 Limiting Distributions 5.3.4 Two Heavy-Tailed Distributions 5.3.5 Exercises 5.4 The Linear Exponential Family 5.4.1 Exercises 6. DISCRETE DISTRIBUTIONS 6.1 Introduction 6.1.1 Exercise 6.2 The Poisson Distribution6.3 The Negative Binomial Distribution 6.4 The Binomial Distribution 6.5 The (a, b,0) Class 6.5.1 Exercises 6.6 Truncation and Modification at zero 6.6.1 Exercises 7. ADVANCED DISCRETE DISTRIBUTIONS 7.1 Compound Frequency Distributions 7.1.1 Exercises 7.2 Further Properties of the Compound Poisson Class 7.2.1 Exercises 7.3 Mixed-Frequency Distributions 7.3.1 The General Mixed-Frequency Distribution 7.3.2 Mixed Poisson Distributions 7.3.3 Exercises 7.4 The Effect of Exposure on Frequency 7.5 An Inventory of Discrete Distributions 7.5.1 Exercises 8. FREQUENCY AND SEVERITY WITHCOVERAGE MODIFICATIONS8.1 Introduction 8.2 Deductibles 8.2.1 Exercises 8.3 The Loss Elimination Ratio and the Effect of Inflation for OrdinaryDeductibles 8.3.1 Exercise 8.4 Policy Limits 8.4.1 Exercises 8.5 Coinsurance, Deductibles, and Limits 8.5.1 Exercises 8.6 The Impact of Deductibles on Claim Frequency 8.6.1 Exercises 9. AGGREGATE LOSS MODELS 9.1 Introduction 9.1.1 Exercises 9.2 Model Choices 9.2.1 Exercises 9.3 The Compound Model for Aggregate Claims 9.3.1 Probabilities and Moments 9.3.2 Stop-Loss Insurance 9.3.3 The Tweedle Distribution A guide that provides in-depth coverage of modelling 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). 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 fifth edition has been updated to reflect these exam changes. 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 and the Canadian Institute of Actuaries • 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. An update of one of the most trusted books on constructing and analyzing actuarial modelsWritten by three renowned authorities in the actuarial field, Loss Models, Third Edition upholds the reputation for excellence that has made this book required reading for the Society of Actuaries (SOA) and Casualty Actuarial Society (CAS) qualification examinations. This update serves as a complete presentation of statistical methods for measuring risk and building models to measure loss in real-world events. This book maintains an approach to modeling and forecasting that utilizes tools related to risk th.