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Pricing Insurance Risk: Theory and Practice [Kõva köide]

  • Formaat: Hardback, 560 pages, kõrgus x laius x paksus: 239x196x33 mm, kaal: 930 g
  • Sari: Wiley Series in Probability and Statistics
  • Ilmumisaeg: 24-May-2022
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119755670
  • ISBN-13: 9781119755678
Teised raamatud teemal:
  • Formaat: Hardback, 560 pages, kõrgus x laius x paksus: 239x196x33 mm, kaal: 930 g
  • Sari: Wiley Series in Probability and Statistics
  • Ilmumisaeg: 24-May-2022
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119755670
  • ISBN-13: 9781119755678
Teised raamatud teemal:
"In order to make insurance a trade at all, the common premium must be sufficient to compensate the common losses, to pay the expense of management, and to afford such a profit as might have been drawn from an equal capital employed in any common trade. Pricing insurance risk is the last mile of underwriting. It determines which risks are accepted onto the balance sheet and makes an insurer's risk appetite operational. It is critical to successful insurance company management. As the last mile, pricing depends on all that has come before. Actuaries and underwriters have analyzed and classified the risk, trended and developed losses, and on-leveled premiums to pick a best-estimate prospective loss cost. Accountants have allocated fixed and variable expenses. Simulation models place the new risk within the context of the company's existing portfolio. The mechanics of all this work is the subject of much of the actuarial education syllabus: experience and exposure rating, predictive analytics, and advanced statistical methods. That is not the subject of this book! All of that prior effort determines the expected loss, and we take it as a given. Pricing adds the risk margin-to afford capital a reasonable return. The risk margin is our subject"--

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.

Preface xii
1 Introduction
1(12)
1.1 Our Subject and Why It Matters
1(1)
1.2 Players, Roles, and Risk Measures
2(2)
1.3 Book Contents and Structure
4(3)
1.4 What's in It for the Practitioner?
7(2)
1.5 Where to Start
9(4)
2 The Insurance Market and Our Case Studies
13(14)
2.1 The Insurance Market
13(2)
2.2 Ins Co.: A One-Period Insurer
15(1)
2.3 Model vs. Reality
16(1)
2.4 Examples and Case Studies
17(8)
2.5 Learning Objectives
25(2)
Part I Risk
27(134)
3 Risk and Risk Measures
29(34)
3.1 Risk in Everyday Life
29(1)
3.2 Defining Risk
30(1)
3.3 Taxonomies of Risk
31(5)
3.4 Representing Risk Outcomes
36(4)
3.5 The Lee Diagram and Expected Losses
40(14)
3.6 Risk Measures
54(6)
3.7 Learning Objectives
60(3)
4 Measuring Risk with Quantiles, VaR, and TVaR
63(42)
4.1 Quantiles
63(7)
4.2 Value at Risk
70(15)
4.3 Tail VaR and Related Risk Measures
85(17)
4.4 Differentiating Quantiles, VaR, and TVaR
102(1)
4.5 Learning Objectives
102(3)
5 Properties of Risk Measures and Advanced Topics
105(42)
5.1 Probability Scenarios
105(5)
5.2 Mathematical Properties of Risk Measures
110(14)
5.3 Risk Preferences
124(6)
5.4 The Representation Theorem for Coherent Risk Measures
130(7)
5.5 Delbaen's Differentiation Theorem
137(4)
5.6 Learning Objectives
141(6)
5.A Lloyd's Realistic Disaster Scenarios
142(1)
5.B Convergence Assumptions for Random Variables
143(4)
6 Risk Measures in Practice
147(10)
6.1 Selecting a Risk Measure Using the Characterization Method
147(1)
6.2 Risk Measures and Risk Margins
148(1)
6.3 Assessing Tail Risk in a Univariate Distribution
149(1)
6.4 The Intended Purpose: Applications of Risk Measures
150(3)
6.5 Compendium of Risk Measures
153(3)
6.6 Learning Objectives
156(1)
7 Guide to the Practice
Chapters
157(4)
Part II Portfolio Pricing
161(146)
8 Classical Portfolio Pricing Theory
163(54)
8.1 Insurance Demand, Supply, and Contracts
163(5)
8.2 Insurer Risk Capital
168(10)
8.3 Accounting Valuation Standards
178(4)
8.4 Actuarial Premium Calculation Principles and Classical Risk Theory
182(4)
8.5 Investment Income in Pricing
186(3)
8.6 Financial Valuation and Perfect Market Models
189(3)
8.7 The Discounted Cash Flow Model
192(8)
8.8 Insurance Option Pricing Models
200(10)
8.9 Insurance Market Imperfections
210(3)
8.10 Learning Objectives
213(4)
8.A Short- and Long-Duration Contracts
215(1)
8.B The Equivalence Principle
216(1)
9 Classical Portfolio Pricing Practice
217(16)
9.1 Stand-Alone Classical PCPs
217(6)
9.2 Portfolio CCoC Pricing
223(1)
9.3 Applications of Classical Risk Theory
224(3)
9.4 Option Pricing Examples
227(4)
9.5 Learning Objectives
231(2)
10 Modern Portfolio Pricing Theory
233(38)
10.1 Classical vs. Modern Pricing and Layer Pricing
233(2)
10.2 Pricing with Varying Assets
235(3)
10.3 Pricing by Layer and the Layer Premium Density
238(1)
10.4 The Layer Premium Density as a Distortion Function
239(6)
10.5 From Distortion Functions to the Insurance Market
245(7)
10.6 Concave Distortion Functions
252(3)
10.7 Spectral Risk Measures
255(4)
10.8 Properties of an SRM and Its Associated Distortion Function
259(2)
10.9 Six Representations of Spectral Risk Measures
261(2)
10.10 Simulation Interpretation of Distortion Functions
263(1)
10.11 Learning Objectives
264(7)
10.A Technical Details
265(6)
11 Modern Portfolio Pricing Practice
271(36)
11.1 Applying SRMs to Discrete Random Variables
271(4)
11.2 Building-Block Distortions and SRMs
275(5)
11.3 Parametric Families of Distortions
280(5)
11.4 SRM Pricing
285(7)
11.5 Selecting a Distortion
292(6)
11.6 Fitting Distortions to Cat Bond Data
298(6)
11.7 Resolving an Apparent Pricing Paradox
304(2)
11.8 Learning Objectives
306(1)
Part III Price Allocation
307(134)
12 Classical Price Allocation Theory
309(30)
12.1 The Allocation of Portfolio Constant CoC Pricing
309(3)
12.2 Allocation of Non-Additive Functionals
312(12)
12.3 Loss Payments in Default
324(2)
12.4 The Historical Development of Insurance Pricing Models
326(11)
12.5 Learning Objectives
337(2)
13 Classical Price Allocation Practice
339(10)
13.1 Allocated CCoC Pricing
339(8)
13.2 Allocation of Classical PCP Pricing
347(1)
13.3 Learning Objectives
348(1)
14 Modern Price Allocation Theory
349(48)
14.1 The Natural Allocation of a Coherent Risk Measure
349(16)
14.2 Computing the Natural Allocations
365(4)
14.3 A Closer Look at Unit Funding
369(16)
14.4 An Axiomatic Approach to Allocation
385(7)
14.5 Axiomatic Characterizations of Allocations
392(2)
14.6 Learning Objectives
394(3)
15 Modern Price Allocation Practice
397(44)
15.1 Applying the Natural Allocations to Discrete Random Variables
397(7)
15.2 Unit Funding Analysis
404(9)
15.3 Bodoff's Percentile Layer of Capital Method
413(8)
15.4 Case Study Exhibits
421(18)
15.5 Learning Objectives
439(2)
Part IV Advanced Topics
441(52)
16 Asset Risk
443(6)
16.1 Background
443(1)
16.2 Adding Asset Risk to Ins Co.
444(3)
16.3 Learning Objectives
447(2)
17 Reserves
449(20)
17.1 Time Periods and Notation
449(1)
17.2 Liability for Ultimate Losses
450(11)
17.3 The Solvency II Risk Margin
461(7)
17.4 Learning Objectives
468(1)
18 Going Concern Franchise Value
469(8)
18.1 Optimal Dividends
469(3)
18.2 The Firm Life Annuity
472(4)
18.3 Learning Objectives
476(1)
19 Reinsurance Optimization
477(6)
19.1 Background
477(1)
19.2 Evaluating Ceded Reinsurance
477(4)
19.3 Learning Objectives
481(2)
20 Portfolio Optimization
483(10)
20.1 Strategic Framework
483(1)
20.2 Market Regulation
484(1)
20.3 Dynamic Capital Allocation and Marginal Cost
485(2)
20.4 Marginal Cost and Marginal Revenue
487(1)
20.5 Performance Management and Regulatory Rigidities
488(2)
20.6 Practical Implications
490(1)
20.7 Learning Objectives
491(2)
A Background Material
493(10)
A.1 Interest Rate, Discount Rate, and Discount Factor
493(1)
A.2 Actuarial vs. Accounting Sign Conventions
493(1)
A.3 Probability Theory
494(6)
A.4 Additional Mathematical Terminology
500(3)
B Notation
503(20)
References
507(16)
Index 523
Stephen J. Mildenhall has extensive general insurance experience, having worked in primary and reinsurance pricing, broking, and education since 1992. He is a Fellow of the Casualty Actuarial Society, an Associate of the Society of Actuaries, and holds a PhD degree in mathematics from the University of Chicago.

John A. Major has served as a research leader and data scientist in diverse insurance contexts, contributing to the state of the art in areas such as claim fraud detection, insurance-linked securities, terrorism risk, and catastrophe modeling. Since 2004, much of his attention has focused on the shareholder value of risk transformation. His publications in over a dozen books and journals have been cited in hundreds of scholarly articles. He is an Associate of the Society of Actuaries and holds a Master's degree in mathematics from Harvard University.