Pricing Insurance Risk: Theory and Practice

✍ Scribed by Stephen J. Mildenhall, John A. Major

• Publisher: Wiley
• Year: 2022
• Tongue: English
• Leaves: 554
• Series: Wiley Series in Probability and Statistics
• Category: Library

✦ Synopsis

PRICING INSURANCE RISK

A comprehensive framework for measuring, valuing, and managing risk

Pricing Insurance Risk: Theory and Practice delivers an accessible and authoritative account of how to determine the premium for a portfolio of non-hedgeable insurance risks and how to allocate it fairly to each portfolio component.

The authors synthesize hundreds of academic research papers, bringing to light little-appreciated answers to fundamental questions about the relationships between insurance risk, capital, and premium. They lean on their industry experience throughout to connect the theory to real-world practice, such as assessing the performance of business units, evaluating risk transfer options, and optimizing portfolio mix.

Readers will discover:

• Definitions, classifications, and specifications of risk
• An in-depth treatment of classical risk measures and premium calculation principles
• Properties of risk measures and their visualization
• A logical framework for spectral and coherent risk measures
• How risk measures for capital and pricing are distinct but interact
• Why the cost of capital, not capital itself, should be allocated
• The natural allocation method and how it unifies marginal and risk-adjusted probability approaches
• Applications to reserve risk, reinsurance, asset risk, franchise value, and portfolio optimization

Perfect for actuaries working in the non-life or general insurance and reinsurance sectors, Pricing Insurance Risk: Theory and Practice is also an indispensable resource for banking and finance professionals, as well as risk management professionals seeking insight into measuring the value of their efforts to mitigate, transfer, or bear nonsystematic risk.

✦ Table of Contents

Pricing Insurance Risk
Contents
Preface
1 Introduction
1.1 Our Subject and Why It Matters
1.2 Players, Roles, and Risk Measures
1.3 Book Contents and Structure
1.4 What's in It for the Practitioner?
1.5 Where to Start
2 The Insurance Market and Our Case Studies
2.1 The Insurance Market
2.2 Ins Co.: A One-Period Insurer
2.3 Model vs. Reality
2.4 Examples and Case Studies
2.5 Learning Objectives
Part I Risk
3 Risk and Risk Measures
3.1 Risk in Everyday Life
3.2 Defining Risk
3.3 Taxonomies of Risk
3.4 Representing Risk Outcomes
3.5 The Lee Diagram and Expected Losses
3.6 Risk Measures
3.7 Learning Objectives
4 Measuring Risk with Quantiles, VaR, and TVaR
4.1 Quantiles
4.2 Value at Risk
4.3 Tail VaR and Related Risk Measures
4.4 Differentiating Quantiles, VaR, and TVaR
4.5 Learning Objectives
5 Properties of Risk Measures and Advanced Topics
5.1 Probability Scenarios
5.2 Mathematical Properties of Risk Measures
5.3 Risk Preferences
5.4 The Representation Theorem for Coherent Risk Measures
5.5 Delbaen's Differentiation Theorem
5.6 Learning Objectives
5.A Lloyd's Realistic Disaster Scenarios
5.B Convergence Assumptions for Random Variables
6 Risk Measures in Practice
6.1 Selecting a Risk Measure Using the Characterization Method
6.2 Risk Measures and Risk Margins
6.3 Assessing Tail Risk in a Univariate Distribution
6.4 The Intended Purpose: Applications of Risk Measures
6.5 Compendium of Risk Measures
6.6 Learning Objectives
7 Guide to the Practice Chapters
Part II Portfolio Pricing
8 Classical Portfolio Pricing Theory
8.1 Insurance Demand, Supply, and Contracts
8.2 Insurer Risk Capital
8.3 Accounting Valuation Standards
8.4 Actuarial Premium Calculation Principles and Classical Risk Theory
8.5 Investment Income in Pricing
8.6 Financial Valuation and Perfect Market Models
8.7 The Discounted Cash Flow Model
8.8 Insurance Option Pricing Models
8.9 Insurance Market Imperfections
8.10 Learning Objectives
8.A Short- and Long-Duration Contracts
8.B The Equivalence Principle
9 Classical Portfolio Pricing Practice
9.1 Stand-Alone Classical PCPs
9.2 Portfolio CCoC Pricing
9.3 Applications of Classical Risk Theory
9.4 Option Pricing Examples
9.5 Learning Objectives
10 Modern Portfolio Pricing Theory
10.1 Classical vs. Modern Pricing and Layer Pricing
10.2 Pricing with Varying Assets
10.3 Pricing by Layer and the Layer Premium Density
10.4 The Layer Premium Density as a Distortion Function
10.5 From Distortion Functions to the Insurance Market
10.6 Concave Distortion Functions
10.7 Spectral Risk Measures
10.8 Properties of an SRM and Its Associated Distortion Function
10.9 Six Representations of Spectral Risk Measures
10.10 Simulation Interpretation of Distortion Functions
10.11 Learning Objectives
10.A Technical Details
11 Modern Portfolio Pricing Practice
11.1 Applying SRMs to Discrete Random Variables
11.2 Building-Block Distortions and SRMs
11.3 Parametric Families of Distortions
11.4 SRM Pricing
11.5 Selecting a Distortion
11.6 Fitting Distortions to Cat Bond Data
11.7 Resolving an Apparent Pricing Paradox
11.8 Learning Objectives
Part III Price Allocation
12 Classical Price Allocation Theory
12.1 The Allocation of Portfolio Constant CoC Pricing
12.2 Allocation of Non-Additive Functionals
12.3 Loss Payments in Default
12.4 The Historical Development of Insurance Pricing Models
12.5 Learning Objectives
13 Classical Price Allocation Practice
13.1 Allocated CCoC Pricing
13.2 Allocation of Classical PCP Pricing
13.3 Learning Objectives
14 Modern Price Allocation Theory
14.1 The Natural Allocation of a Coherent Risk Measure
14.2 Computing the Natural Allocations
14.3 A Closer Look at Unit Funding
14.4 An Axiomatic Approach to Allocation
14.5 Axiomatic Characterizations of Allocations
14.6 Learning Objectives
15 Modern Price Allocation Practice
15.1 Applying the Natural Allocations to Discrete Random Variables
15.2 Unit Funding Analysis
15.3 Bodoff's Percentile Layer of Capital Method
15.4 Case Study Exhibits
15.5 Learning Objectives
Part IV Advanced Topics
16 Asset Risk
16.1 Background
16.2 Adding Asset Risk to Ins Co.
16.3 Learning Objectives
17 Reserves
17.1 Time Periods and Notation
17.2 Liability for Ultimate Losses
17.3 The Solvency II Risk Margin
17.4 Learning Objectives
18 Going Concern Franchise Value
18.1 Optimal Dividends
18.2 The Firm Life Annuity
18.3 Learning Objectives
19 Reinsurance Optimization
19.1 Background
19.2 Evaluating Ceded Reinsurance
19.3 Learning Objectives
20 Portfolio Optimization
20.1 Strategic Framework
20.2 Market Regulation
20.3 Dynamic Capital Allocation and Marginal Cost
20.4 Marginal Cost and Marginal Revenue
20.5 Performance Management and Regulatory Rigidities
20.6 Practical Implications
20.7 Learning Objectives
A Background Material
A.1 Interest Rate, Discount Rate, and Discount Factor
A.2 Actuarial vs. Accounting Sign Conventions
A.3 Probability Theory
A.4 Additional Mathematical Terminology
B Notation
References
Index
ELUA