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
