Modern Actuarial Theory and Practice, Second Edition

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ISBN: 9781584883685 | 1584883685
Cover: Hardcover
Copyright: 12/28/2004

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In the years since the publication of the first edition of this best-selling text, the incorporation of ideas and theories from the rapidly growing field of financial economics has precipitated considerable development of thinking in the actuarial profession. Modern Actuarial Theory and Practice, Second Edition integrates those changes and presents an up-to-date, comprehensive overview of UK and international actuarial theory, practice and modeling. It describes all of the traditional areas of actuarial activity, but in a manner that highlights the fundamental principles of actuarial theory and practice as well as their economic, financial, and statistical foundations.

Part I: Investment

The Widening Scope of Actuarial Theory and Practice

(20)

Introduction

(2)

Financial Intermediaries: Their Role in Resolving the ``Constitutional Weakness''

(1)

Functional Approach to the Analysis of Intermediaries

(2)

Intermediating Functions of Banks

(1)

Intermediating Functions of Insurers

(1)

Intermediating Functions of Unit Trusts and Mutual Funds

(1)

Banks, Insurance Companies and Pension Funds: Fundamental Similarities and Differences

(1)

Bank Loans, Credit Risk and Insurance

(2)

The Evolving Relationship Banking and Insurance

(3)

Some Examples of the Evolving Product Links between Banks and Non-banks

(3)

Conclusion

(4)

References

(3)

Investments and Valuation

(42)

Introduction

(1)

Cash Instruments

(2)

General Characteristics

(1)

Specific Cash Instruments and Valuation Issues

(1)

Risk Characteristics

(1)

General Characteristics of Conventional Bonds

(9)

Government Bonds

(1)

Corporate Bonds

(1)

Bond Valuation

(2)

Economic Analysis

(4)

Risk Characteristics

(1)

General Characteristics of Index-Linked Bonds

(7)

Index-Linked Bond Valuation

(1)

Economic Analysis

(1)

Risk Characteristics

(1)

Estimating Market Expectations of Inflation Using Market Information

(3)

General Characteristics of Foreign Currency Bonds

(2)

Valuation

(1)

Economic Analysis

(1)

Risk Characteristics

(1)

General Characteristics of Equity Investment

(6)

Equity Valuation

(3)

Economic Analysis

(1)

Risk Analysis

(1)

Real-Estate Investment

(5)

Valuation

(2)

Economic Analysis

(1)

Risk Analysis

(1)

International Equity Investment

(2)

International Equity Valuation

(1)

Economic Analysis

(1)

Risk Analysis

(1)

Derivatives

(9)

General Characteristics

(2)

Valuation

(2)

Risk Characteristics

(1)

References

(4)

General Principles of Asset Allocation

(62)

Introduction

(1)

Investment Risk

(8)

Matching Asset and Liability Characteristics

(2)

Matching Asset and Liability Terms

(1)

Matching by Currency

(1)

Diversification

(1)

Short-Term Volatility Risk

(2)

Risk of Long-Term Underperformance

(1)

Equity Volatility in the Short Term and the Long Term

(1)

Default Risk

(1)

Prospective Returns

(15)

Relationship between Risk and Return

(2)

Returns from Bonds and Cash Instruments

(5)

Returns from Equity and Real-Estate Investments

(1)

Prospective Rates of Return and Investment Decision-Making

(1)

The Real Yield Gap

(2)

Relative Value of Index-Linked and Conventional Bonds

(2)

The Yield Gap

(2)

Comparing Other Investment Categories

(1)

Institutional and Governmental Influences and Constraints

(4)

Marketability, Liquidity, and Transaction Costs

(1)

Legal Constraints

(1)

Taxation

(1)

Policyholder Preferences

(1)

The Use of Derivative Instruments

(1)

Asset Allocation Principles Applied to Pension Funds

(10)

Mechanism for Taking Investment Decisions

(1)

Liability and Other Financial Considerations

(6)

Legislation and Taxation Considerations

(1)

Expected Investment Returns

100

(1)

Size of Fund

101

(1)

Marketability and Liquidity

101

(1)

Summary of Considerations

102

(1)

International Differences

102

(1)

Life Insurance Companies

103

(9)

Liability Considerations

104

(2)

Options and Guarantees

106

(1)

Free Reserves

107

(1)

Expected Returns

107

(1)

Legislation

108

(1)

Professional Guidance to the Actuary

109

(1)

Taxation

110

(1)

Marketability and Liquidity

110

(1)

Summary of Considerations

111

(1)

International Differences

112

(1)

Nonlife Insurance Companies

112

(6)

Liability Considerations

113

(1)

The Place of Equities, Real Estate and Index-Linked Government Bonds in a Nonlife Portfolio: The Role of the Solvency Margin

114

(2)

Foreign Currency Investment

116

(1)

Legislation

116

(1)

Taxation Considerations

117

(1)

Marketability and Liquidity

117

(1)

Expected Investment Returns

117

(1)

Summary of Considerations

118

(1)

Personal Investments

118

(5)

Unit Trusts and Investment Funds

118

(3)

Personal Pensions

121

(2)

Conclusion

123

(4)

References

123

(4)

Investment Risk

127

(16)

Introduction

127

(1)

Utility Theory and Risk Measures

127

(5)

Relating Utility Functions to Risk Aversion and the Risk Premium

130

(2)

Summary Risk Measures

132

(5)

Standard Deviation of Returns

132

(1)

Downside/Shortfall Risk Measures

133

(2)

Value at Risk

135

(1)

Practical Issues when Calculating VaR

136

(1)

Tail Loss

137

(1)

Combining Risk and Return Measures

137

(1)

Coherent Risk Measures

138

(1)

The Use of Shortfall Constraints

139

(1)

Conclusion

140

(3)

References

141

(2)

Portfolio Selection Techniques and Investment Modeling

143

(54)

Introduction

143

(1)

Immunization

143

(5)

Derivation of Conditions

143

(3)

Observations on the Theory of Immunization

146

(1)

The Usefulness of Immunization in Practice

147

(1)

Modern Portfolio Theory

148

(9)

Portfolio Diversification

148

(3)

Efficient Portfolios

151

(1)

Capital Market Line

152

(3)

The Capital Asset Pricing Model

155

(1)

Modern Portfolio Theory: Insights and Limitations

155

(2)

Extension of Portfolio Theory to Include Actuarial Liabilities

157

(7)

Portfolio Optimization in the Presence of Liabilities

157

(2)

Connections Between Redington and the Wise--Wilkie Approach

159

(1)

Generalization of Portfolio Optimization in the Presence of Liabilities

159

(3)

Portfolio Selection in an Asset/Liability Framework Using a Generalized Approach to Risk

162

(2)

Stochastic Investment Models

164

(14)

Economic Investment Models

165

(2)

Statistical Investment Models

167

(3)

Statistical Models with Shocks

170

(1)

The Wilkie Stochastic Investment Model

171

(7)

Asset Liability Modeling

178

(4)

Conclusion

182

(15)

Appendix A. The Wilkie Model: A Case Study

182

(10)

References

192

(5)

Part II: Life Insurance

Fundamental Features of Life Insurance

197

(22)

Introduction

197

(1)

Basic Contract Structures

198

(2)

Term, Term-Life or Temporary Assurance

198

(1)

Whole Life Assurance

198

(1)

Endowment Assurance

199

(1)

Annuity

199

(1)

Life Insurance Products

200

(3)

Product Distribution

201

(2)

Who Initiates the Sale?

203

(1)

Taxation of Long-Term Business

203

(1)

Supervision and Regulation

203

(4)

Solvency Regulation

204

(1)

Regulation of Selling Practices

204

(1)

Other Areas of Regulation

205

(1)

The Influence of Professional and Ethical Practice

205

(1)

Provision of Compensation

206

(1)

Life Office Ownership

207

(1)

Long-Term Insurance Risk Management

207

(12)

Personal Risk Management

207

(1)

Insurance Company Risk

208

(1)

Managing Insurance Risk: Risk Pooling

209

(3)

The Influence of Modern Product Designs on Life Insurance Company Risk

212

(5)

Managing the office

217

(1)

References

218

(1)

Nonparticipating Life Insurance

219

(34)

Conventional Nonparticipating Contracts

219

(12)

Operation of the Fund

219

(4)

Reserving and Profit Recognition: Realistic Basis

223

(6)

Reserving on the Premium Basis

229

(1)

Cash Values

230

(1)

Linked Accumulating Nonparticipating Contracts

231

(20)

Operation of the Fund

232

(8)

Reserving for Unit-Linked Business

240

(4)

Actuarial Funding

244

(4)

Unit-Linked Business with Level Initial Expense Charges

248

(2)

Discontinuance Terms for Unit-Linked Policies

250

(1)

Nonlinked Accumulating Nonparticipating Contracts

251

(2)

References

252

(1)

Participating Life Insurance

253

(28)

Different Distribution Methods

253

(6)

Contribution Method

254

(1)

Uniform Reversionary Bonus Method

255

(1)

Revalorization Methods

256

(2)

Accumulating with Profits

258

(1)

Profit Distribution Strategies

259

(3)

History

259

(1)

Profit Deferral

260

(1)

Profit Smoothing

260

(2)

Discontinuance Terms for With-Profits Policies

262

(1)

Overall Operation of a With-Profits Fund

263

(2)

Numerical Example

263

(2)

Determining Dividends or Bonus Rates

265

(8)

Contribution Method

265

(1)

Revalorization Methods

266

(1)

Reversionary Bonus Method

266

(4)

Accumulating With-Profits Method

270

(3)

Reserving for With-Profits: Earned Profit Reserves

273

(5)

Example: Reversionary Bonus Method

273

(3)

Example: Accumulating With-Profits Method

276

(2)

Distribution of Shareholders' Profits

278

(1)

A Comment on Meeting Consumer Needs

279

(2)

References

279

(2)

The Regulation of Solvency and its Effect on the Emergence of Profit

281

(22)

The Statutory Solvency Assessment

281

(4)

Statutory Reserving Requirements

282

(2)

Breaching the Supervisory Solvency Regulations

284

(1)

Dynamic Solvency Testing

285

(1)

The Valuation of the Liabilities

285

(5)

The Valuation Method

285

(4)

The Valuation Assumptions

289

(1)

The Effects of the Statutory Solvency Requirements on Life Office Operation

290

(13)

Non-Profit Business

290

(5)

Conventional With-Profits Business

295

(4)

Other Types of With-Profits Business

299

(1)

Unit-Linked Business

300

(1)

References

301

(2)

Life Office Risks and Risk Management

303

(36)

The Interested Parties

303

(2)

Policyholders' Interests

303

(2)

Shareholders' Interests

305

(1)

Regulators' Interests

305

(1)

The Nature of the Risks

305

(2)

Risk Control

307

(1)

Insurance Risk

308

(11)

Underwriting and Risk Classification

309

(4)

Financial Underwriting

313

(1)

Reinsurance

314

(5)

Business Risk

319

(20)

Expense Risk

320

(5)

Discontinuance Risk

325

(2)

New-Business (Valuation Strain) Risk

327

(5)

Other New Business Risks

332

(1)

Distribution Risk

333

(2)

Risks From Policyholder Options and Guarantees

335

(1)

Data Risks

335

(1)

Taxation Risk

336

(1)

References

337

(2)

The Actuarial Role in Life Office Management

339

(30)

Introduction

339

(1)

Product Pricing

340

(12)

The Control Cycle

340

(5)

Profit Testing

345

(1)

Whole-Office Pricing

346

(2)

The Model Office

348

(3)

Use of the Model Office in Pricing

351

(1)

Analysis of Surplus

352

(2)

Monitoring and Updating the Assumptions in the Control Cycle

354

(1)

Further Uses of Model Offices in Actuarial Management

355

(9)

To Assess Solvency

355

(3)

To Investigate Profit Distribution Policy

358

(2)

To Investigate Investment Policy

360

(1)

To Investigate Business Risks

360

(3)

To Estimate Reserves

363

(1)

To Estimate Risk-Based Capital

363

(1)

Choice of Stochastic Model

364

(1)

Modeling Risk

364

(5)

References

365

(4)

Part III: General Insurance

Introduction to General Insurance

369

(20)

Background

369

(3)

Exposure Measurement

370

(1)

The Evaluation and Identification of Factors Influencing the Degree of Risk

371

(1)

The Range of Events Giving Rise to a Liability under the Contract

371

(1)

Risks and Their Management

372

(3)

The Contract

375

(2)

Reinsurance: Insurance for Insurers

377

(1)

Management of General Insurance

378

(1)

Providers of Insurance

379

(4)

The Direct Market

380

(1)

London Market

381

(1)

Other Providers

382

(1)

The Insurance Broker

382

(1)

The Insurance Environment and the Provision of Capital

383

(2)

Conclusions

385

(4)

Appendix A

385

(2)

References

387

(2)

General Insurance Accounts

389

(14)

The Purpose of Accounts

389

(3)

The Accounting Framework

392

(7)

The Balance Sheet

393

(1)

The Revenue Account

394

(2)

The Profit and Loss Account

396

(1)

Some Key Analytical Statistics

397

(2)

Conclusions

399

(4)

Appendix A

400

(2)

References

402

(1)

Premium Rating

403

(46)

Introduction and Basic Ideas

403

(3)

Basic Premium Formula

406

(6)

Insurance Levies

408

(1)

Contingency Loading

409

(3)

Acquisition Costs

412

(1)

Estimating the Office Premium

412

(21)

The Risk Premium, and Approaches to Calculating the Expected Claims

412

(2)

Risk Factors and Rating Factors

414

(4)

Exposure Measurement and Analyzing Past Exposure

418

(3)

Statistical Modeling

421

(4)

Claims Data

425

(6)

Deriving Expected Claims

431

(2)

Measuring Expenses

433

(3)

Direct Expenses

435

(1)

Indirect Expenses

436

(1)

Experience Rating

436

(4)

Experience Rating by Claim Number

437

(1)

Experience Rating by Claim Cost

438

(2)

Business Planning

440

(4)

Monitoring Experience

442

(2)

Conclusions

444

(5)

Appendix A

444

(2)

Appendix B

446

(1)

References

447

(2)

Reinsurance

449

(42)

Introduction

449

(7)

Why Buy Reinsurance?

449

(3)

Some Background

452

(4)

Contractual Relationships: A Comparison of Co-Insurance and Reinsurance

456

(2)

Reinsurance Arrangements

458

(2)

Descriptions of Each Type of Reinsurance

460

(17)

Proportional Reinsurance

460

(3)

Nonproportional Reinsurance

463

(11)

Order of Application of Reinsurances

474

(3)

Practical Considerations of Reinsurance Program Design

477

(10)

Past Practice and the Structure of the Existing Program

478

(1)

Underwriting Guidelines, Maximum Line Sizes and Exposures and Changes in the Guidelines

478

(1)

Changes in the Basis on Which Cover Has Been Written

479

(1)

Expected Business Volumes and New Business Areas

479

(1)

The Availability of Reinsurance Cover, the Cost of Reinsurance, and the Market Cycle

479

(1)

Desire to Develop Relationships with Certain Reinsurers or Cedants and Reciprocation Opportunities

480

(1)

Operational and Financial Considerations

480

(1)

Relationships with the Reinsurance Broker

481

(1)

Changes in Management Structure

481

(1)

Alternatives to Reinsurance

482

(3)

Practical Issues in Managing the Reinsurance Asset

485

(2)

Conclusions

487

(4)

Appendix A

487

(2)

References

489

(2)

Reserving

491

(68)

Introduction

491

(1)

Reserves Carried

492

(17)

Reserves in Respect of Unexpired or Unearned Exposure

493

(5)

Contingent Reserves

498

(4)

Reserves in Respect of Earned Exposure

502

(5)

Reserving Exercise: The Basic Steps

507

(2)

Form of the Data

509

(7)

The Choice of Year of Origin or Claim Cohort

516

(4)

Reporting Period

516

(1)

Accident Period

517

(1)

Underwriting Period or Policy Period

518

(2)

Reserving Methods

520

(34)

The Basic Chain Ladder Method

520

(8)

Inflation-Adjusted Chain Ladder Method

528

(5)

Separation Technique

533

(3)

Average Cost per Claim

536

(4)

The Loss Ratio and Bornheutter--Ferguson Method

540

(2)

Operational Time Model

542

(2)

The Bootstrap Method

544

(3)

Distribution-Free Approach

547

(2)

Approaches to Reserving Using Formal Statistical Models

549

(4)

Summary of Reserve Calculations

553

(1)

Conclusions

554

(5)

References

554

(5)

Part IV: Pensions

Types of Pension Plan

559

(20)

Classification of Plans

559

(4)

Introduction

559

(1)

Single-Member Plans

560

(1)

Group Pension Plans

561

(1)

State Pension Plans

562

(1)

Defined-Benefit Plans

563

(6)

Benefit Formulae

563

(1)

Salary-Linked Benefits

563

(2)

Retirement Benefits

565

(1)

Death Benefits

566

(1)

Withdrawal Benefits

567

(1)

Pension Increases

567

(1)

Cash Benefits on Retirement

568

(1)

Member Contributions

568

(1)

State Pension Benefits

568

(1)

Defined Contribution Plans

569

(4)

Types of Contribution Formula

569

(1)

Money Purchase Principle

570

(2)

Member's Pension Choices

572

(1)

Hybrid Plans

573

(6)

Benefit Underpins

574

(1)

Cash-Balance Plans

574

(1)

With-Profits Fund

575

(1)

References

576

(3)

Actuarial Modeling of Defined-Benefit Plans

579

(56)

Cash-Flow Projections

579

(10)

A Simple Model Plan

579

(1)

Projection of Benefit Outgo

580

(2)

Cash-Flow Equation

582

(1)

Stationary Fund Equation

583

(2)

Example of Cash-Flow Calculations

585

(4)

Practical Value of Cash-Flow Projections

589

(1)

The Actuarial Valuation

589

(35)

Objectives of Actuarial Valuation

590

(1)

Valuation Assumptions

591

(1)

Valuation Formulae

592

(5)

Actuarial Funding Methods

597

(6)

Example Illustrating Different Funding Methods

603

(2)

Valuation of Assets

605

(7)

Example Illustrating Alternative Asset Valuation Methods

612

(4)

Analysis of Surplus

616

(4)

Example of Analysis of Surplus

620

(4)

Actuarial Benefit Calculations

624

(4)

Transfer Values

624

(2)

Voluntary Early Retirement

626

(1)

Commutation

627

(1)

Unfunded Plans

628

(7)

Pay-As-You-Go Principle

628

(1)

Dependency Ratio

629

(1)

Demographic Factors

630

(1)

Economic Factors

630

(1)

Methods of Cost Control

631

(1)

The Future of Unfunded Social Security Plans

632

(1)

References

632

(3)

Investment Strategies for Defined-Benefit Plans

635

(28)

Introduction

635

(1)

Characteristics of Different Assets

636

(2)

Equities

636

(1)

Government Bonds

636

(1)

Corporate Bonds

637

(1)

Real Estate and Related Assets

637

(1)

Cash

638

(1)

Objectives of Investment Strategy

638

(6)

Maximizing Expected Returns

638

(1)

Matching Liabilities

639

(3)

Portfolio Diversification

642

(1)

Liquidity

643

(1)

Stochastic Asset/Liability Modeling

644

(13)

Performance Measures

645

(1)

Modeling Tools

646

(4)

A Simple Example Based on Mean-Variance Analysis

650

(5)

Combining Funding and Investment Decisions

655

(2)

Practical Issues

657

(6)

Who Controls the Investment Policy?

657

(1)

Who Owns the Surplus?

658

(1)

Tax Considerations

658

(1)

Legal Constraints on Investment Policy

659

(2)

References

661

(2)

Individual Pension Choices

663

(32)

Introduction

663

(1)

Projection of Money-Purchase Benefits

664

(10)

Deterministic Projections

665

(4)

Examples of Deterministic Benefit Projections

669

(2)

Stochastic Projections

671

(1)

Example Illustrating Stochastic Benefit Projections

672

(2)

Annuity Choices for Pensioners

674

(8)

Whether and When to Buy an Annuity

674

(2)

Example Illustrating Calculation of Break-Even Return

676

(1)

Level or Increasing Annuity

677

(1)

Example Illustrating Calculation of Break-Even Lifespan

678

(1)

Stochastic Approaches

679

(2)

Example Illustrating Stochastic Approach

681

(1)

Utility-Maximization Models

682

(13)

Expected Utility Theory

682

(1)

Utility of Lifetime Consumption

683

(2)

Utility of Retirement Wealth

685

(1)

Example Based on Utility of Retirement Wealth

686

(5)

References

691

(4)

Part V: Health Insurance

An Introduction to Health Insurance

695

(10)

Background

695

(1)

Actuarial Control Cycle

695

(1)

Basic Contract Structures of Health Insurance Products

696

(1)

Income Protection Insurance

696

(1)

Critical Illness Insurance

697

(1)

Long-Term Care Insurance

697

(1)

Private Medical Insurance

697

(1)

Comparison between Life and Health Insurance

697

(1)

External Factors Affecting Health Insurance

698

(1)

Demography

698

(1)

Economic Climate

698

(1)

State Provision of Health Care and Services

699

(1)

Features of Health Insurance

699

(2)

Deferred Period

699

(1)

Guaranteed and Reviewable Premiums

700

(1)

Claims Management

700

(1)

Risks to the Insurer

701

(1)

Adverse Selection

701

(1)

Moral Hazard

701

(1)

Mismatch of Claim Definitions

702

(1)

Medical Advances

702

(1)

Reinsurance

702

(3)

References

703

(2)

Income Protection Insurance

705

(22)

Introduction

705

(1)

Changing Demography

706

(1)

Changing Attitude to Disability

706

(1)

The Nature of Disability

706

(1)

The Evolution of the Product

706

(2)

Product Design

708

(4)

Benefit Types

708

(1)

Definitions of Disability

709

(2)

Group Business

711

(1)

Underwriting

712

(1)

Pricing

712

(7)

Risk Factors

713

(1)

Data Sources

714

(1)

Trends

715

(1)

Guarantees

715

(1)

Variations

715

(1)

Pricing Methodology

716

(3)

Claims

719

(2)

Claims Management

719

(2)

Claims Data

721

(1)

Reserving

721

(2)

Reserves in Respect of Active Lives

722

(1)

Reserves in Respect of Claimants

722

(1)

Contingency Reserves

723

(1)

Conclusion

723

(4)

Appendix A: Inception Rate and Disabled Annuity Method

723

(1)

Appendix B: Manchester Unity Method

724

(1)

References

725

(2)

Critical Illness

727

(20)

Introduction

727

(1)

Product Structure

728

(2)

Acceleration Benefit

728

(1)

Stand-Alone Benefit

728

(1)

Other Types of Critical Illness Product

729

(1)

Policy Content

730

(3)

Conditions Covered

730

(1)

Defining the Conditions

731

(1)

Standardization of Policy Wording: The U.K. Example

732

(1)

Underwriting Critical Illness Policies

733

(1)

Pricing the Risk

734

(8)

Risk Factors

734

(2)

Data Sources and Difficulties

736

(2)

Trends

738

(1)

Guarantees

738

(1)

Variations in Claims Experience

738

(1)

Pricing Methodology

738

(4)

Claims

742

(1)

Claims Management

742

(1)

Causes of Claim

742

(1)

Reserving

742

(1)

Conclusion

743

(4)

Appendix A

744

(1)

References

745

(2)

Long-Term Care

747

(18)

Introduction

747

(1)

Funding Long-Term Care

748

(2)

Background

748

(1)

Brief International Overview of Long-Term Care Funding

748

(2)

Pre-Funded Long-Term Care Insurance Products

750

(8)

Claim Triggers

750

(1)

Stand-Alone Insurance Products

751

(1)

Long-Term Care Insurance as a Rider Benefit

752

(1)

Underwriting

752

(1)

Pricing the Risk

753

(3)

Sales and Marketing

756

(1)

Claims

756

(2)

Reserving

758

(1)

Alternatives to Pre-Funded Insurance Products

758

(3)

Noninstitutionalized Settings for Long-Term Care

758

(1)

Use of Equity in Property to Fund Long Term Care: The U.K. Example

759

(2)

Conclusion

761

(4)

References

762

(3)

Private Medical Insurance

765

(20)

Introduction

765

(1)

Product Design

766

(4)

General Design Principles

766

(1)

Private Medical Insurance Products: The U.K. Example

767

(3)

Group Business

770

(1)

Underwriting

771

(2)

Declared Medical History

772

(1)

Moratorium

772

(1)

Premium Loadings

772

(1)

Pricing

773

(6)

Data Sources

773

(1)

Pricing Methodology

774

(1)

Medical Expense Inflation

775

(2)

Risk Factors

777

(1)

Guarantees

778

(1)

No-Claims Discount

779

(1)

Claims

779

(2)

The Nature of the Claim

779

(1)

Claims Control

779

(1)

Claims Procedures

780

(1)

Reserving

781

(1)

Claims Reported but Not Settled

781

(1)

Claims Incurred but Not Reported

782

(1)

Unearned Premium Reserve

782

(1)

Unexpired Risk Reserve

782

(1)

Policy Specific Reserves

782

(1)

Conclusion

782

(3)

References

783

(2)

Index

785

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Modern Actuarial Theory and Practice, Second Edition

Summary

Table of Contents

Supplemental Materials