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Pricing in General Insurance, 2nd Edition

Name: Pricing in General Insurance, 2nd Edition
Author: Pietro Parodi
ISBN: 9781000860832

by Pietro Parodi

May 2023

Intermediate to advanced

738 pages

22h 58m

English

Chapman and Hall/CRC

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Cover
Half-Title Page
Title Page
Copyright Page
Dedication
Table of Contents
Preface to the Second Edition
Biography
Preface to the First Edition
1 The Pricing Process: A Gentle Start
1.1 Pricing in Economic Theory 1.2 Exposure Rating 1.3 Experience Rating 1.3.1 Risk Costing (Gross) 1.3.2 Risk Costing (Ceded) 1.3.3 Determining the Technical Premium 1.3.4 Commercial Considerations and the Actual Premium 1.3.5 Limitations of this Elementary Pricing Example 1.4 Mixing Exposure and Experience Rating 1.5 High-Level Pricing Process 1.5.1 Portfolio Pricing Process 1.6 Questions

Part I Background and Context
2 Insurance and Reinsurance Products
2.1 Classification of General Insurance Products: General Ideas 2.2 Products by Category of Cover 2.2.1 Property Insurance 2.2.2 Liability Insurance 2.2.3 Financial Loss Insurance 2.2.4 Fixed Benefits Insurance 2.2.5 ‘Packaged’ Products 2.3 Products by Type of Customer 2.3.1 Personal Lines 2.3.2 Commercial Lines 2.3.3 Reinsurance 2.4 Standard Classification Schemes 2.5 Questions
3 The Cover Structure
3.1 Personal Lines 3.1.1 Purpose of the Excess Amount 3.1.2 Purpose of the Limit 3.2 Commercial Lines 3.2.1 Policy Bases 3.2.2 Basic Policy Structure 3.2.3 Excess Insurance 3.2.4 Other Coverage Modifiers 3.3 Reinsurance 3.3.1 Treaty-Specific Policy Bases 3.3.2 Non-Proportional Reinsurance 3.3.3 Proportional Reinsurance 3.4 Questions
4 The Insurance Markets
4.1 Major Participants in the Insurance Market 4.1.1 Buyers of Insurance 4.1.2 Insurers 4.1.3 Intermediaries 4.2 Major Insurance Markets 4.2.1 London Market 4.2.2 Bermuda and Similar Markets 4.3 How Is Insurance Sold? 4.3.1 Personal Lines 4.3.2 Commercial Lines and Reinsurance 4.4 Underwriting Cycle 4.4.1 How Does the Underwriting Cycle Affect Pricing? 4.5 Questions
5 Pricing in Context
5.1 Regulatory Environment 5.1.1 Product Restrictions 5.1.2 Premium Restrictions 5.1.3 Information Restriction 5.1.4 Capital Requirements 5.2 Legal Environment 5.2.1 Changes in the Legal Environment May Increase or Decrease the Number and Severity of Claims 5.2.2 Court Rulings Filter Down to Out-of-Court Claims 5.2.3 Lost in Translation 5.2.4 Court Inflation 5.2.5 General Trends in Behaviour and Awareness 5.3 Larger Economy 5.3.1 How Does This Affect Pricing? 5.4 Investment Conditions 5.4.1 How Does This Affect Pricing? 5.5 Currency Movements 5.5.1 How Does This Affect Pricing? 5.6 Natural Environment 5.6.1 Weather 5.6.2 Space Weather 5.6.3 Natural Catastrophes 5.6.4 How Does This Affect Pricing? 5.7 Pricing in the Corporate Context 5.7.1 Planning Function 5.7.2 Underwriting Function 5.7.3 Claims Function 5.7.4 Actuarial: Reserving 5.7.5 Actuarial: Capital Modelling 5.7.6 Finance 5.7.7 Management Information 5.7.8 Investment Function 5.7.9 Reinsurance Function 5.7.10 Risk Management Function 5.7.11 Other Functions 5.8 Other Things You Need to Keep Up With 5.9 Questions
Part II The Generic Experience Rating Process
6 The Scientific Basis for Pricing: : Risk Theory
6.1 Aggregate Loss Models 6.1.1 Individual Risk Model 6.1.2 Collective Risk Model 6.1.3 Extensions of the Collective and Individual Risk Models 6.2 Applications to Risk Costing 6.3 Risk Costing Process for the Frequency/Severity Model 6.4 Questions
7 Familiarise Yourself with the Risk
7.1 Things to Look Out for (Commercial Lines/Reinsurance) 7.1.1 What Does the Client Do, That Is, What Is Its Business? 7.1.2 What Are the Client’s Main Location(s) and Jurisdiction(s)? 7.1.3 What Are the Client’s Main ‘Numbers’ (Exposures and Financials)? 7.1.4 Have There Been Any Notable Changes in the Risk Profile of the Client over Time? 7.1.5 Industry-Related Questions 7.1.6 Sources of Knowledge on the Risk 7.2 Things to Look Out for (Personal Lines) 7.3 Questions
8 Data Requirements for Pricing
8.1 Policy and Cover Data 8.2 Claims Data 8.3 Exposure Data 8.3.1 What Is Exposure? 8.3.2 Exposure Data for Experience Rating 8.3.3 Exposure Data for Exposure Rating 8.4 Portfolio and Market Data 8.5 Questions
9 Setting the Loss Inflation Assumptions
9.1 Sources of Inflation Information 9.2 Data-Driven Estimates of Loss Inflation 9.2.1 Statistical Estimation of Loss Inflation Using Robust Statistics 9.2.2 Basket Method, Based on Selected Samples 9.2.3 Statistical Approach to Large-Loss Inflation 9.3 Questions
10 Data Preparation
10.1 Data Cleansing 10.2 Loss Data Transformation 10.2.1 Loss Revaluation 10.2.2 Currency Conversion 10.2.3 Policy Year Allocation 10.2.4 Individual Loss Adjustments for Exposure Changes 10.3 Exposure Data Transformation 10.3.1 Matching Exposure to Losses 10.3.2 Exposure On-Levelling 10.4 Data Summarisation 10.5 Questions
11 The Burning Cost Approach
11.1 Burning Cost Methodology 11.1.1 Data and Assumptions 11.1.2 Input to the Burning Cost Analysis 11.1.3 Step A: Revalue Losses and Apply Policy Modifiers to All Claims 11.1.4 Step B: Aggregate Loss by Policy Year 11.1.5 Step C: Adjust for Exposure Changes 11.1.6 Step D: Make Adjustments for IBNR 11.1.7 Step E: Make Adjustments for Large Losses 11.1.8 Step F: Make Other Adjustments 11.1.9 Step G: Impose Aggregate Deductibles/Limits as Necessary 11.1.10 Step H: Calculate the Burning Cost Estimate of the Expected Losses 11.1.11 Step I: Premium Calculation Based on the Burning Cost *11.1.12 Summary: Burning Cost Analysis in Formulae 11.2 Adjusting for IBNR: Development Triangles 11.3 Producing an Aggregate Loss Distribution 11.4 Burning Cost for Portfolio Pricing 11.4.1 The Concept of Earned Amount 11.4.2 Earned Amount Calculations 11.4.3 Burning Cost Analysis (Occurrence-Based Policies) 11.5 The Limitations of Burning Cost Analysis 11.6 Questions
12 What Is This Thing Called Modelling?: A Gentle Introduction to Machine Learning
12.1 Why Do We Need Modelling at All? 12.1.1 Models Allow Us to Make Predictions That Generalise Loss Experience 12.1.2 Other Uses of Models 12.2 The Modelling Approach 12.3 How Do You Select a Good Model? A Foray into Machine Learning 12.3.1 Model Selection Concepts Through a Simple Example 12.4 Actuarial Applications of Machine Learning Concepts/Techniques 12.5 Further Readings on the Application of Machine Learning to Actuarial Modelling
13 Frequency Modelling: Adjusting for Claim Count IBNR
13.1 Input to IBNR Adjustment 13.2 Triangle Development Methods for IBNR Estimation 13.2.1 Method 1: Ignore the Last Diagonal 13.2.2 Method 2: Gross Up the Last Diagonal 13.2.3 Method 3: Choose an ‘Ad Hoc’ Observation Period 13.2.4 Method 4: Shift the Observation Period 13.2.5 Method 5: Shift the Development Period 13.2.6 Comparison of Methods 1 through 5 13.3 Triangle-Free Methodology for IBNR Estimation 13.3.1 A Simple Special Case: Exponential Delays with Uniform Exposure *13.3.2 Estimating the Reporting Delay Distribution (General Case) *13.3.3 Projecting Claim Counts to Ultimate (General Case) *13.3.4 Uncertainty *13.3.5 A Fat-Tailed Model for the Delay Distribution 13.3.6 Calculations in Practice – An Example 13.3.7 Analysis of Zero Claims 13.3.8 Comparison between the Triangle-Free Approach and the Triangle-Based Approach to IBNR 13.4 Questions
14 Frequency Modelling: Selecting and Calibrating a Frequency Model
14.1 Binomial Distribution and the Multivariate Bernoulli Distribution 14.1.1 Simulating from a Binomial Distribution 14.1.2 Generalisation: The Multivariate Bernoulli Distribution1 14.2 Poisson Distribution 14.2.1 Facts about the Poisson Distribution 14.2.2 Simulating from a Poisson Distribution 14.2.3 How Do You Calculate λ? 14.3 Negative Binomial Distribution 14.3.1 Technical Generalities 14.3.2 Simulating from a Negative Binomial Distribution 14.3.3 Fitting a Negative Binomial (i.e. Calculating r and β) to Past Claim Counts 14.4 Selecting a Frequency Model 14.4.1 The Issues with Using the Variance/Mean Ratio as a Selection Criterion 14.4.2 Theoretical Arguments that Should Drive Model Selection 14.4.3 Recommended Approach to Frequency Modelling 14.5 Results of the Frequency Analysis for Our Case Study 14.6 Calibrating a Frequency Model with No Losses 14.6.1 Heuristic Rules for Selecting a Value of λ in the Case of No Losses 14.6.2 The Amending Function Approach 14.7 Questions
15 Severity Modelling: Adjusting for IBNER and Other Factors
15.1 Introduction 15.2 Methods for Identifying and Dealing with IBNER 15.2.1 Method 1: Ignore IBNER 15.2.2 Method 2: Just Use Closed Claims 15.2.3 Method 3: Identify Trends and Adjust for IBNER 15.3 Comparison of Different Methods 15.3.1 Method 1: Ignore IBNER 15.3.2 Method 2: Just Use Closed Claims 15.3.3 Method 3a: Identify Trends and Adjust for IBNER by Using Development Triangles 15.3.4 Method 3b: Identify Trends and Adjust for IBNER by Using GLM-Like Techniques 15.4 Questions
16 Severity Modelling: Selecting and Calibrating a Severity Model
16.1 Input to Severity Modelling 16.2 Choosing the Right Severity Model: A Subtle Problem 16.2.1 General Rules for Model Selection 16.2.2 Experiment Revisited 16.3 Modelling Large (‘Tail’) Losses: Extreme Value Theory 16.3.1 Pickand–Balkema–de Haan Theorem 16.3.2 Identifying the Extreme Value Region 16.3.3 Creating a Spliced Small/Large Loss Distribution 16.3.4 Calculating the Values of the Parameters 16.3.5 Extreme Value Theory: Actual Practice 16.3.6 Limitations of Extreme Value Theory 16.4 A Simple Strategy for Modelling Ground-Up Losses 16.4.1 Application to a Real-World Case Study 16.4.2 Kolmogorov–Smirnov Test 16.4.3 Moving Beyond the Lognormal Model 16.5 Using Portfolio/Market Data 16.5.1 Advantages of Using Market Data for Tail Modelling 16.5.2 Disadvantages of Using External Data for Tail Modelling 16.6 Appendix A: Kolmogorov–Smirnov Test 16.7 Questions
17 Aggregate Loss Modelling
17.1 ‘Exact’ Solution for the Collective Risk Model (Gross Losses) 17.2 Parametric Approximations 17.2.1 Gaussian Approximation 17.2.2 Other Parametric Approximations *17.3 Numerical Quasi-Exact Methods (Gross Losses) *17.3.1 Fast Fourier Transform Method *17.3.2 Panjer Recursion 17.4 Monte Carlo Simulation (Gross Losses) 17.4.1 Practical Issues 17.4.2 Implementation 17.5 Coverage Modifications (Ceded and Retained Losses) 17.5.1 Gaussian Approximation *17.5.2 Fast Fourier Transform *17.5.3 Panjer Recursion 17.5.4 The Monte Carlo Simulation 17.6 A Comparison of the Different Methods at a Glance 17.6.1 Conclusions 17.7 Monte Carlo Simulation Results for our Case Study 17.8 Monte Carlo Simulation for the Individual Risk Model 17.9 Example Code 17.10 Questions
18 Identifying, Measuring, and Communicating Uncertainty
18.1 Process Uncertainty 18.1.1 How to Calculate Its Effect 18.1.2 How to Communicate It 18.2 Parameter Uncertainty 18.2.1 How to Calculate Its Effect 18.2.2 How to Communicate It 18.3 Model Uncertainty 18.3.1 How to Calculate Its Effect 18.3.2 How to Communicate It 18.4 Assumption/Data Uncertainty 18.4.1 How to Calculate Its Effect 18.4.2 How to Communicate It 18.5 Approximation Errors in calculations 18.5.1 How to Calculate Its Effect 18.5.2 How to Communicate It 18.6 Applications to the Risk Costing Process 18.7 Questions
19 Setting the Premium
19.1 Cost Plus Methodology in Detail 19.1.1 Expected Losses 19.1.2 Allowance for Uncertainty 19.1.3 Other Costs 19.1.4 Investment Income 19.1.5 Loading for Profit/Cost of Capital 19.1.6 Technical Premium Formula 19.1.7 Actual Premium Charged 19.2 Capital Considerations in Pricing 19.2.1 Overall Methodology 19.2.2 Risk Measures 19.2.3 Capital Allocation Methods 19.3 Price Optimisation 19.3.1 Determining the Demand Function 19.3.2 Maximising the Total Expected Profits 19.3.3 Limitations 19.3.4 Other Considerations/Approaches 19.4 Questions
20 The Pricing Cycle and Rate Change Calculations
20.1 The Pricing Control Cycle 20.1.1 Product Pricing 20.1.2 Pricing as a Cycle 20.2 Rate Adequacy Monitoring 20.3 Rate Change Calculations – Generalities and Non-Actuarial Approach 20.3.1 Uses and Perspectives 20.3.2 Terminology and Notation 20.3.3 Non-Actuarial Rate Change Calculations 20.4 Actuarial Rate Change Calculations (Single Contract or Contractual Unit) 20.4.1 Other Sources of Change 20.4.2 A Note on Model Changes 20.4.3 A Note on Loss History 20.4.4 A Note on Loadings 20.4.5 Gross vs Net Rate Change Calculations 20.4.6 Relationship to the Premium Adequacy Index 20.5 Breaking Down the Premium Change into Its Components 20.5.1 Taking External Expenses into Account in the Walk from AP to AP' 20.6 The Loss Ratio Walk 20.7 Rate Change at Programme and Portfolio Level 20.7.1 Combining the Rate Change of Different Contract Units *20.7.2 Layer Mapping 20.8 A Worked-Out Example 20.8.1 Rate Change Calculations and Premium Walk for Each Contract 20.8.2 Portfolio Rate Change Calculations 20.8.3 Premium Adequacy Calculations 20.8.4 Interpretation of Results 20.9 Questions
Part III Business-Specific Pricing
21 Experience Rating for Non-Proportional Reinsurance
21.1 Types of Contract 21.2 Inputs 21.2.1 Policy Information 21.2.2 Claims Data 21.2.3 Exposure Data 21.3 Frequency Analysis 21.3.1 Exposure and Contract Basis 21.3.2 Incorporating Rate Changes When Using Original Premium as Exposure 21.3.3 IBNR Analysis 21.3.4 Selection of a Frequency Model 21.4 Severity Analysis 21.4.1 IBNER Analysis 21.4.2 Selecting and Calibrating a Severity Model 21.5 Payment and Settlement Pattern Analysis 21.5.1 Settlement Pattern 21.5.2 Payment Pattern 21.6 Aggregate Losses to an Excess Layer 21.6.1 Analytical Calculation of Expected Losses and Variance for a Layer 21.6.2 Aggregate Loss Distribution to a Layer via Monte Carlo Simulation 21.7 Technical Premium Calculations 21.7.1 No Reinstatement Premiums, Index Clause 21.7.2 Reinstatement Premiums, No Index Clause 21.8 Questions
22 Exposure Rating for Property Insurance
22.1 Inadequacy of Standard Experience Rating for Property Risks 22.2 How Exposure Curves Arise 22.3 Relationship with Severity Curves 22.4 Properties of Exposure Curves 22.5 Commonly Used Curves and Bernegger’s Parameterisation 22.5.1 Bernegger (MBBEFD) Curves 22.5.2 Properties of Bernegger’s Curves 22.5.3 Simulating Losses Using a Bernegger Distribution 22.6 Build and Calibrate Your Own Exposure Curve 22.6.1 How Can You Calibrate an Exposure Curve if You Don’t Have the MPLs? 22.7 Exposure Rating Process in Reinsurance 22.7.1 Basic Process 22.7.2 How This Is Done in Practice 22.7.3 Simulation of the Aggregate Loss Distribution 22.8 Exposure Rating in Direct Insurance 22.8.1 Ingredients to Pricing 22.8.2 Pricing Methodology 22.8.3 Hybrid Experience/Exposure Rating for Property: Basic Algorithm *22.8.4 Non-Scalable Losses and MPL Uncertainty: Relaxing the Assumptions Behind Exposure Rating 22.9 Questions
23 Liability Rating Using Increased Limit Factor Curves
23.1 How ILF Curves Arise 23.1.1 Assumptions Underlying ILF Curves 23.1.2 Definition of ILF Curves 23.1.3 Relationship with Severity Curves 23.2 Applications to Pricing 23.3 Effect of Claims Inflation on ILF Curves 23.4 Derivation of ILF Curves 23.4.1 Derivation of ILF Curves from a Severity Model 23.4.2 ISO Methodology for the Derivation of ILF Curves 23.5 Other Issues 23.5.1 Indexation Clause 23.5.2 Discounting 23.5.3 Dealing with Expenses 23.5.4 Per Claim versus Per Occurrence Basis 23.6 Riebesell (ILF) Curves 23.7 Do We Really Need ILF Curves? 23.8 Questions
24 Pricing Considerations for Specific Lines of Business
24.1 Professional Indemnity Cover 24.1.1 Legal Framework 24.1.2 Policy 24.1.3 Calculating Reporting Year Exposure 24.1.4 Frequency Analysis 24.1.5 Severity Analysis 24.1.6 Systemic Effects 24.1.7 Aggregate Loss Analysis 24.1.8 Recap on Professional Indemnity 24.2 Weather Derivatives 24.2.1 What Needs Weather Derivatives Respond To 24.2.2 What Weather Derivatives Are 24.2.3 Market for Weather Derivatives 24.2.4 Basis Risk 24.2.5 Valuation of Weather Derivatives 24.2.6 Actuarial Valuation Method in Detail 24.3 Credit Risk 24.3.1 Data Requirements 24.3.2 Pricing Methodology 24.4 Extended Warranty 24.4.1 Data Requirements 24.4.2 Failure Rate Analysis 24.4.3 Frequency Analysis: From Failure Rate to Expected Claim Count 24.4.4 Severity Analysis 24.4.5 Aggregate Loss Model 24.4.6 Systemic Factors 24.4.7 Rating Factor Analysis 24.4.8 Pricing 24.5 Miscellaneous Classes of Business 24.5.1 Aviation Insurance 24.5.2 Business Interruption 24.5.3 Commercial Motor Insurance 24.5.4 Product Liability 24.5.5 Construction Cover 24.6 Questions
25 Catastrophe Modelling in Pricing
25.1 Structure of a Catastrophe Model 25.1.1 Hazard Module 25.1.2 Vulnerability Module 25.1.3 The Financial Module 25.2 Other Outputs of a Catastrophe Model 25.2.1 Occurrence Exceedance Probability 25.2.2 Aggregate Exceedance Probability 25.2.3 Return Period 25.2.4 Average Annual Loss 25.2.5 Standard Deviation 25.2.6 Period Loss Tables (PLTs) and Year Loss Tables (YLTs) 25.3 Key Perils Modelled 25.4 Pricing Using Cat Rates and Hazard Maps 25.5 Pricing Using Cat Models: Simulation of Cat Loss Scenarios and PLTs 25.5.1 Inputs to a Catastrophe Model 25.5.2 Simulating Cat Losses Using ELTs 25.5.3 Simulating Using the Period Loss Tables (PLTs) 25.5.4 Combining Non-Catastrophe and Catastrophe Losses 25.6 Calculation of the Severity Distribution 25.7 What Role for Actuaries? 25.8 Questions
Part IV General-Purpose Techniques
26 Credibility Theory
26.1 The General Idea of Credibility 26.1.1 Expected Loss Rate 26.1.2 Client’s ‘True’ Expected Loss Rate 26.1.3 Client’s Estimated Expected Loss Rate, and Its Uncertainty 26.1.4 Portfolio Benchmark 26.1.5 Credibility Rate 26.2 Examples and Applications 26.2.1 A Simple Example 26.2.2 Credibility of a Frequency/Severity Model 26.2.3 Mixing Experience and Exposure Rating 26.3 Specific Approaches to Credibility 26.3.1 Classical Credibility 26.3.2 Bayesian Credibility 26.3.3 Bühlmann Credibility 26.3.4 Bühlmann–Straub Credibility 26.4 Limitations of the Credibility Approach 26.5 Questions
27 Rating Factor Selection and Calibration: GLMs, GAMs, and Regularisation
27.1 Why Rating Factors Are Useful 27.1.1 Some Facts about Rating Factors in Practice 27.2 Non-Actuarial Approach to Models with Rating Factors 27.3 How Do We Develop a Rating-Factor Model in Practice? From One-Way Analysis to Generalised Linear Models 27.3.1 One-Way Analysis 27.3.2 Multi-Way Analysis 27.4 Generalised Linear Modelling 27.4.1 Least Squares Regression and Multivariate Linear Modelling 27.4.2 Beyond the Linear Model: Generalised Linear Models 27.4.3 Frequently Used Models for Pricing 27.4.4 Model Structuring 27.4.5 Model Selection 27.4.6 Model Structure Validation 27.4.7 A Practical General Insurance Example: Modelling Claims Frequency for Motor Insurance 27.5 Generalised Additive Models (GAMs) 27.5.1 What is the Difference Between GLMs and GAMs? 27.5.2 Cubic Splines 27.5.3 A Simple Example of an Interpolating Spline 27.5.4 Smoothing (Regression) Splines 27.5.5 Practical Example 27.6 Other Machine Learning Techniques for Rating 27.7 Questions
28 Multilevel Factors and Smoothing
28.1 Credibility Smoothing 28.1.1 An Example: Car Model Codes 28.1.2 Credibility Smoothing and the GLM Approach 28.2 Spatial Smoothing 28.2.1 One-Dimensional Analogy 28.2.2 Distance-Based Smoothing 28.2.3 Adjacency-Based Smoothing 28.2.4 Degree of Smoothing 28.2.5 Spatial Smoothing and the GLM Approach 28.3 Machine Learning Techniques 28.4 Questions
29 Pricing Multiple Lines of Business and Risks
29.1 Divide and Conquer? 29.2 Independent Case 29.2.1 Combining Aggregate Loss Models by the Monte Carlo Simulation *29.2.2 Combining Aggregate Loss Models by FFT 29.2.3 Limitations 29.3 Measuring Dependency 29.3.1 Rank Correlation 29.3.2 Tail Dependence 29.4 Modelling Dependency with Copulas 29.4.1 An Intuitive Approach to Copulas 29.4.2 Notable Examples of Copulas 29.5 Aggregate Loss Distribution of Two Correlated Risks 29.5.1 Correlating the Severities of Two Risks 29.5.2 Correlating the Frequencies 29.5.3 Correlating the Total Losses of Two Risks *29.6 Aggregate Loss Distribution of an Arbitrary Number of Correlated Risks 29.7 Common Shock Modelling 29.7.1 Common Shock Model 29.7.2 Binary Common Shocks 29.8 R Code for Generating an Arbitrary Number of Variables Correlated through a t Copula 29.9 Questions
30 Insurance Structure Optimisation
30.1 Efficient Frontier Approach 30.1.1 Cost of Insurance 30.1.2 Benefits of Insurance 30.1.3 Efficient Structures 30.1.4 Limitations of the Efficient Frontier Approach 30.2 Minimising the Total Cost of (Insurable) Risk 30.2.1 Risk Management Options 30.2.2 Total Cost of Risk: Definition 30.2.3 Choosing the Optimal Structure 30.2.4 Total Cost of Risk Calculation: A Simple Example 30.2.5 Relationship between Total Cost of Risk and Efficient Frontier 30.2.6 Limitations 30.3 Questions
31 An Introduction to Pricing Models
31.1 Generalities 31.2 Exposure-Based Models 31.2.1 M 0 – The Simplest Possible Model? 31.2.2 M 1 – An Example of an Exposure-based Deterministic Model 31.2.3 M 2 – An Example of an Exposure-Based Stochastic Model 31.2.4 Exposure Models for different Types of Business 31.2.5 Characteristics of a Mature Exposure-based Pricing Model 31.3 Experience-Based Models 31.3.1 Structure of an Experience Rating Model 31.3.2 M 5 – A Simple Experience Rating Model: Burning Cost Model 31.3.3 M 6 – A Simple Frequency/Severity Experience Rating Model 31.3.4 User-Machine Interaction in Experience Rating Tools 31.4 Hybrid Exposure/Experience Models 31.5 Pricing Models by Type of Undertaking 31.5.1 Personal Lines Insurance 31.5.2 Commercial Lines Insurance 31.5.3 Reinsurance 31.6 Rate Change Calculations 31.7 Model Calibration 31.7.1 The Use of Expert Judgment in Calibration 31.8 Model Governance 31.8.1 The Model Landscape 31.8.2 Model Development Guidelines 31.9 Questions
References
Index

Content preview from Pricing in General Insurance, 2nd Edition

23Liability Rating Using Increased Limit Factor Curves

DOI: 10.1201/9781003168881-26

We have seen how exposure rating works with property type of cover. In this chapter we consider what you could loosely call exposure rating for liability cover. The method is based on the use of the so-called increased limit factor (ILF) reference curves (Miccolis 1977; Palmer 2006; Riegel 2008). The key idea behind ILF curves is that they should help you determine how the expected losses increase by increasing the limit purchased, and ultimately that helps you determine the cost of a specific layer of (re)insurance based on the rate per unit of exposure at a given limit.

We’ll start by looking at how ILF curves arise (Section 23.1), and then we’ll look ...

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Pricing in General Insurance, 2nd Edition

by Pietro Parodi

23Liability Rating Using Increased Limit Factor Curves

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